id	sid	tid	token	lemma	pos
ajbmeb-2644	1	1	american	american	PROPN
ajbmeb-2644	1	2	journal	journal	PROPN
ajbmeb-2644	1	3	of	of	ADP
ajbmeb-2644	1	4	business	business	NOUN
ajbmeb-2644	1	5	management	management	NOUN
ajbmeb-2644	1	6	,	,	PUNCT
ajbmeb-2644	1	7	economics	economic	NOUN
ajbmeb-2644	1	8	and	and	CCONJ
ajbmeb-2644	1	9	banking	banking	NOUN
ajbmeb-2644	1	10	issn	issn	PROPN
ajbmeb-2644	1	11	(	(	PUNCT
ajbmeb-2644	1	12	e	e	NOUN
ajbmeb-2644	1	13	):	):	PUNCT
ajbmeb-2644	1	14	2832	2832	NUM
ajbmeb-2644	1	15	-	-	SYM
ajbmeb-2644	1	16	8078	8078	NUM
ajbmeb-2644	1	17	volume	volume	NOUN
ajbmeb-2644	1	18	32	32	NUM
ajbmeb-2644	1	19	,	,	PUNCT
ajbmeb-2644	1	20	|	|	ADV
ajbmeb-2644	1	21	january	january	PROPN
ajbmeb-2644	1	22	2025	2025	NUM
ajbmeb-2644	1	23	p	p	NOUN
ajbmeb-2644	1	24	a	a	DET
ajbmeb-2644	1	25	g	g	NOUN
ajbmeb-2644	1	26	e	e	NOUN
ajbmeb-2644	1	27	|	|	ADV
ajbmeb-2644	1	28	31	31	NUM
ajbmeb-2644	1	29	www.americanjournal.org	www.americanjournal.org	NOUN
ajbmeb-2644	1	30	logarithmic	logarithmic	ADJ
ajbmeb-2644	1	31	functions	function	NOUN
ajbmeb-2644	1	32	,	,	PUNCT
ajbmeb-2644	1	33	equations	equation	NOUN
ajbmeb-2644	1	34	and	and	CCONJ
ajbmeb-2644	1	35	inequalities	inequality	NOUN
ajbmeb-2644	1	36	abdullayev	abdullayev	PROPN
ajbmeb-2644	1	37	nurbek	nurbek	PROPN
ajbmeb-2644	1	38	shuhrat	shuhrat	NOUN
ajbmeb-2644	1	39	o'g'li	o'g'li	PROPN
ajbmeb-2644	1	40	ro'ziqulov	ro'ziqulov	PROPN
ajbmeb-2644	1	41	sa'dulla	sa'dulla	PROPN
ajbmeb-2644	1	42	egamnazar	egamnazar	NOUN
ajbmeb-2644	2	1	o'g'li	o'g'li	PROPN
ajbmeb-2644	2	2	tursunov	tursunov	VERB
ajbmeb-2644	2	3	zohidjon	zohidjon	NOUN
ajbmeb-2644	2	4	tohirjon	tohirjon	NOUN
ajbmeb-2644	2	5	ògli	ògli	NOUN
ajbmeb-2644	2	6	a	a	DET
ajbmeb-2644	2	7	b	b	PROPN
ajbmeb-2644	2	8	s	s	ADP
ajbmeb-2644	2	9	t	t	PROPN
ajbmeb-2644	2	10	r	r	NOUN
ajbmeb-2644	2	11	a	a	DET
ajbmeb-2644	2	12	c	c	NOUN
ajbmeb-2644	2	13	t	t	NOUN
ajbmeb-2644	2	14	k	k	X
ajbmeb-2644	2	15	e	e	PROPN
ajbmeb-2644	2	16	y	y	PROPN
ajbmeb-2644	2	17	w	w	NOUN
ajbmeb-2644	3	1	o	o	NOUN
ajbmeb-2644	3	2	r	r	NOUN
ajbmeb-2644	3	3	d	d	PROPN
ajbmeb-2644	3	4	s	s	VERB
ajbmeb-2644	3	5	this	this	DET
ajbmeb-2644	3	6	article	article	NOUN
ajbmeb-2644	3	7	provides	provide	VERB
ajbmeb-2644	3	8	information	information	NOUN
ajbmeb-2644	3	9	on	on	ADP
ajbmeb-2644	3	10	logarithmic	logarithmic	ADJ
ajbmeb-2644	3	11	functions	function	NOUN
ajbmeb-2644	3	12	,	,	PUNCT
ajbmeb-2644	3	13	equations	equation	NOUN
ajbmeb-2644	3	14	,	,	PUNCT
ajbmeb-2644	3	15	and	and	CCONJ
ajbmeb-2644	3	16	solutions	solution	NOUN
ajbmeb-2644	3	17	to	to	ADP
ajbmeb-2644	3	18	inequalities	inequality	NOUN
ajbmeb-2644	3	19	.	.	PUNCT
ajbmeb-2644	4	1	logarithmic	logarithmic	ADJ
ajbmeb-2644	4	2	functions	function	NOUN
ajbmeb-2644	4	3	,	,	PUNCT
ajbmeb-2644	4	4	equations	equation	NOUN
ajbmeb-2644	4	5	,	,	PUNCT
ajbmeb-2644	4	6	inequalities	inequality	NOUN
ajbmeb-2644	4	7	,	,	PUNCT
ajbmeb-2644	4	8	graph	graph	NOUN
ajbmeb-2644	4	9	,	,	PUNCT
ajbmeb-2644	4	10	function	function	NOUN
ajbmeb-2644	4	11	,	,	PUNCT
ajbmeb-2644	4	12	interval	interval	NOUN
ajbmeb-2644	4	13	positive	positive	ADJ
ajbmeb-2644	4	14	.	.	PUNCT
ajbmeb-2644	5	1	introduction	introduction	NOUN
ajbmeb-2644	5	2	logarithmic	logarithmic	ADJ
ajbmeb-2644	5	3	function	function	NOUN
ajbmeb-2644	5	4	.	.	PUNCT
ajbmeb-2644	6	1	let	let	VERB
ajbmeb-2644	6	2	a	a	DET
ajbmeb-2644	6	3	>	>	X
ajbmeb-2644	6	4	0	0	NUM
ajbmeb-2644	6	5	,	,	PUNCT
ajbmeb-2644	6	6	a	a	DET
ajbmeb-2644	6	7	≠	≠	PROPN
ajbmeb-2644	6	8	1	1	NUM
ajbmeb-2644	6	9	.	.	PUNCT
ajbmeb-2644	7	1	given	give	VERB
ajbmeb-2644	7	2	that	that	SCONJ
ajbmeb-2644	7	3	the	the	DET
ajbmeb-2644	7	4	number	number	NOUN
ajbmeb-2644	7	5	n	n	PART
ajbmeb-2644	7	6	is	be	AUX
ajbmeb-2644	7	7	a	a	DET
ajbmeb-2644	7	8	logarithm	logarithm	NOUN
ajbmeb-2644	7	9	on	on	ADP
ajbmeb-2644	7	10	the	the	DET
ajbmeb-2644	7	11	basis	basis	NOUN
ajbmeb-2644	7	12	a	a	X
ajbmeb-2644	7	13	,	,	PUNCT
ajbmeb-2644	7	14	the	the	DET
ajbmeb-2644	7	15	number	number	NOUN
ajbmeb-2644	7	16	a	a	PRON
ajbmeb-2644	7	17	is	be	AUX
ajbmeb-2644	7	18	said	say	VERB
ajbmeb-2644	7	19	to	to	PART
ajbmeb-2644	7	20	be	be	AUX
ajbmeb-2644	7	21	the	the	DET
ajbmeb-2644	7	22	degree	degree	NOUN
ajbmeb-2644	7	23	indicator	indicator	NOUN
ajbmeb-2644	7	24	that	that	PRON
ajbmeb-2644	7	25	needs	need	VERB
ajbmeb-2644	7	26	to	to	PART
ajbmeb-2644	7	27	be	be	AUX
ajbmeb-2644	7	28	raised	raise	VERB
ajbmeb-2644	7	29	to	to	PART
ajbmeb-2644	7	30	form	form	VERB
ajbmeb-2644	7	31	the	the	DET
ajbmeb-2644	7	32	number	number	NOUN
ajbmeb-2644	7	33	n	n	CCONJ
ajbmeb-2644	7	34	,	,	PUNCT
ajbmeb-2644	7	35	and	and	CCONJ
ajbmeb-2644	7	36	is	be	AUX
ajbmeb-2644	7	37	denoted	denote	VERB
ajbmeb-2644	7	38	by	by	ADP
ajbmeb-2644	7	39	logan	logan	PROPN
ajbmeb-2644	7	40	.	.	PUNCT
ajbmeb-2644	8	1	by	by	ADP
ajbmeb-2644	8	2	definition	definition	NOUN
ajbmeb-2644	8	3	,	,	PUNCT
ajbmeb-2644	8	4	ax	ax	NOUN
ajbmeb-2644	8	5	=	=	SYM
ajbmeb-2644	8	6	n	n	PROPN
ajbmeb-2644	8	7	(	(	PUNCT
ajbmeb-2644	8	8	a	a	PRON
ajbmeb-2644	8	9	>	>	X
ajbmeb-2644	8	10	0	0	NUM
ajbmeb-2644	8	11	,	,	PUNCT
ajbmeb-2644	8	12	a	a	DET
ajbmeb-2644	8	13	1	1	NUM
ajbmeb-2644	8	14	1	1	NUM
ajbmeb-2644	8	15	)	)	PUNCT
ajbmeb-2644	8	16	is	be	AUX
ajbmeb-2644	8	17	the	the	DET
ajbmeb-2644	8	18	x	x	ADJ
ajbmeb-2644	8	19	solution	solution	NOUN
ajbmeb-2644	8	20	of	of	ADP
ajbmeb-2644	8	21	the	the	DET
ajbmeb-2644	8	22	equation	equation	NOUN
ajbmeb-2644	8	23	x	x	PUNCT
ajbmeb-2644	8	24	=	=	PUNCT
ajbmeb-2644	8	25	logan	logan	PROPN
ajbmeb-2644	8	26	number	number	NOUN
ajbmeb-2644	8	27	.	.	PUNCT
ajbmeb-2644	9	1	the	the	DET
ajbmeb-2644	9	2	action	action	NOUN
ajbmeb-2644	9	3	of	of	ADP
ajbmeb-2644	9	4	finding	find	VERB
ajbmeb-2644	9	5	the	the	DET
ajbmeb-2644	9	6	logarithm	logarithm	NOUN
ajbmeb-2644	9	7	of	of	ADP
ajbmeb-2644	9	8	an	an	DET
ajbmeb-2644	9	9	expression	expression	NOUN
ajbmeb-2644	9	10	is	be	AUX
ajbmeb-2644	9	11	called	call	VERB
ajbmeb-2644	9	12	logarithm	logarithm	NOUN
ajbmeb-2644	9	13	of	of	ADP
ajbmeb-2644	9	14	the	the	DET
ajbmeb-2644	9	15	same	same	ADJ
ajbmeb-2644	9	16	expression	expression	NOUN
ajbmeb-2644	9	17	,	,	PUNCT
ajbmeb-2644	9	18	while	while	SCONJ
ajbmeb-2644	9	19	finding	find	VERB
ajbmeb-2644	9	20	the	the	DET
ajbmeb-2644	9	21	same	same	ADJ
ajbmeb-2644	9	22	expression	expression	NOUN
ajbmeb-2644	9	23	itself	itself	PRON
ajbmeb-2644	9	24	according	accord	VERB
ajbmeb-2644	9	25	to	to	ADP
ajbmeb-2644	9	26	a	a	DET
ajbmeb-2644	9	27	given	give	VERB
ajbmeb-2644	9	28	logarithm	logarithm	NOUN
ajbmeb-2644	9	29	is	be	AUX
ajbmeb-2644	9	30	called	call	VERB
ajbmeb-2644	9	31	potentiation	potentiation	NOUN
ajbmeb-2644	9	32	.	.	PUNCT
ajbmeb-2644	10	1	when	when	SCONJ
ajbmeb-2644	10	2	the	the	DET
ajbmeb-2644	10	3	expression	expression	NOUN
ajbmeb-2644	10	4	x	x	PUNCT
ajbmeb-2644	10	5	=	=	PUNCT
ajbmeb-2644	10	6	logan	logan	PROPN
ajbmeb-2644	10	7	is	be	AUX
ajbmeb-2644	10	8	potentiated	potentiate	VERB
ajbmeb-2644	10	9	,	,	PUNCT
ajbmeb-2644	10	10	a	a	DET
ajbmeb-2644	10	11	recursive	recursive	ADJ
ajbmeb-2644	10	12	n	n	NOUN
ajbmeb-2644	10	13	=	=	NOUN
ajbmeb-2644	10	14	ax	ax	NOUN
ajbmeb-2644	10	15	is	be	AUX
ajbmeb-2644	10	16	formed	form	VERB
ajbmeb-2644	10	17	.	.	PUNCT
ajbmeb-2644	11	1	with	with	ADP
ajbmeb-2644	11	2	a	a	DET
ajbmeb-2644	11	3	>	>	X
ajbmeb-2644	11	4	0	0	NUM
ajbmeb-2644	11	5	,	,	PUNCT
ajbmeb-2644	11	6	a	a	DET
ajbmeb-2644	11	7	≠	≠	PROPN
ajbmeb-2644	11	8	1	1	NUM
ajbmeb-2644	11	9	,	,	PUNCT
ajbmeb-2644	11	10	and	and	CCONJ
ajbmeb-2644	11	11	n	n	CCONJ
ajbmeb-2644	11	12	>	>	ADP
ajbmeb-2644	11	13	0	0	NUM
ajbmeb-2644	11	14	,	,	PUNCT
ajbmeb-2644	11	15	the	the	DET
ajbmeb-2644	11	16	equations	equation	NOUN
ajbmeb-2644	11	17	ax	ax	NOUN
ajbmeb-2644	11	18	=	=	PUNCT
ajbmeb-2644	11	19	n	n	NOUN
ajbmeb-2644	11	20	and	and	CCONJ
ajbmeb-2644	11	21	logan	logan	PROPN
ajbmeb-2644	12	1	=	=	PUNCT
ajbmeb-2644	12	2	x	x	NOUN
ajbmeb-2644	12	3	are	be	AUX
ajbmeb-2644	12	4	of	of	ADP
ajbmeb-2644	12	5	equal	equal	ADJ
ajbmeb-2644	12	6	strength	strength	NOUN
ajbmeb-2644	12	7	.	.	PUNCT
ajbmeb-2644	13	1	thus	thus	ADV
ajbmeb-2644	13	2	we	we	PRON
ajbmeb-2644	13	3	have	have	VERB
ajbmeb-2644	13	4	a	a	DET
ajbmeb-2644	13	5	function	function	NOUN
ajbmeb-2644	13	6	y	y	PROPN
ajbmeb-2644	13	7	=	=	PUNCT
ajbmeb-2644	13	8	logax	logax	PROPN
ajbmeb-2644	13	9	(	(	PUNCT
ajbmeb-2644	13	10	a	a	PRON
ajbmeb-2644	13	11	>	>	X
ajbmeb-2644	13	12	0	0	NUM
ajbmeb-2644	13	13	,	,	PUNCT
ajbmeb-2644	13	14	a	a	DET
ajbmeb-2644	13	15	≠	≠	PROPN
ajbmeb-2644	13	16	1	1	NUM
ajbmeb-2644	13	17	)	)	PUNCT
ajbmeb-2644	13	18	that	that	PRON
ajbmeb-2644	13	19	is	be	AUX
ajbmeb-2644	13	20	continuous	continuous	ADJ
ajbmeb-2644	13	21	and	and	CCONJ
ajbmeb-2644	13	22	monotonic	monotonic	ADJ
ajbmeb-2644	13	23	in	in	ADP
ajbmeb-2644	13	24	its	its	PRON
ajbmeb-2644	13	25	field	field	NOUN
ajbmeb-2644	13	26	of	of	ADP
ajbmeb-2644	13	27	detection	detection	NOUN
ajbmeb-2644	13	28	.	.	PUNCT
ajbmeb-2644	14	1	this	this	DET
ajbmeb-2644	14	2	function	function	NOUN
ajbmeb-2644	14	3	:	:	PUNCT
ajbmeb-2644	14	4	a	a	DET
ajbmeb-2644	14	5	basis	basis	NOUN
ajbmeb-2644	14	6	is	be	AUX
ajbmeb-2644	14	7	called	call	VERB
ajbmeb-2644	14	8	a	a	DET
ajbmeb-2644	14	9	logarithmic	logarithmic	ADJ
ajbmeb-2644	14	10	function	function	NOUN
ajbmeb-2644	14	11	.	.	PUNCT
ajbmeb-2644	15	1	the	the	DET
ajbmeb-2644	15	2	y	y	PROPN
ajbmeb-2644	15	3	=	=	NOUN
ajbmeb-2644	15	4	logax	logax	ADJ
ajbmeb-2644	15	5	function	function	NOUN
ajbmeb-2644	15	6	is	be	AUX
ajbmeb-2644	15	7	the	the	DET
ajbmeb-2644	15	8	inverse	inverse	ADJ
ajbmeb-2644	15	9	function	function	NOUN
ajbmeb-2644	15	10	to	to	ADP
ajbmeb-2644	15	11	the	the	DET
ajbmeb-2644	15	12	y	y	NOUN
ajbmeb-2644	15	13	=	=	NOUN
ajbmeb-2644	15	14	ax	ax	NOUN
ajbmeb-2644	15	15	function	function	NOUN
ajbmeb-2644	15	16	.	.	PUNCT
ajbmeb-2644	16	1	its	its	PRON
ajbmeb-2644	16	2	graph	graph	NOUN
ajbmeb-2644	16	3	is	be	AUX
ajbmeb-2644	16	4	generated	generate	VERB
ajbmeb-2644	16	5	by	by	ADP
ajbmeb-2644	16	6	a	a	DET
ajbmeb-2644	16	7	symmetric	symmetric	ADJ
ajbmeb-2644	16	8	substitution	substitution	NOUN
ajbmeb-2644	16	9	of	of	ADP
ajbmeb-2644	16	10	the	the	DET
ajbmeb-2644	16	11	function	function	NOUN
ajbmeb-2644	16	12	graph	graph	NOUN
ajbmeb-2644	16	13	y	y	NOUN
ajbmeb-2644	16	14	=	=	NOUN
ajbmeb-2644	16	15	ax	ax	NOUN
ajbmeb-2644	16	16	with	with	ADP
ajbmeb-2644	16	17	respect	respect	NOUN
ajbmeb-2644	16	18	to	to	ADP
ajbmeb-2644	16	19	the	the	DET
ajbmeb-2644	16	20	straight	straight	ADJ
ajbmeb-2644	16	21	line	line	NOUN
ajbmeb-2644	17	1	y	y	PROPN
ajbmeb-2644	17	2	=	=	PUNCT
ajbmeb-2644	17	3	x.	x.	NOUN
ajbmeb-2644	17	4	since	since	SCONJ
ajbmeb-2644	17	5	the	the	DET
ajbmeb-2644	17	6	logarithmic	logarithmic	ADJ
ajbmeb-2644	17	7	function	function	NOUN
ajbmeb-2644	17	8	is	be	AUX
ajbmeb-2644	17	9	an	an	DET
ajbmeb-2644	17	10	inverse	inverse	NOUN
ajbmeb-2644	17	11	function	function	NOUN
ajbmeb-2644	17	12	to	to	ADP
ajbmeb-2644	17	13	the	the	DET
ajbmeb-2644	17	14	exponential	exponential	ADJ
ajbmeb-2644	17	15	function	function	NOUN
ajbmeb-2644	17	16	,	,	PUNCT
ajbmeb-2644	17	17	its	its	PRON
ajbmeb-2644	17	18	properties	property	NOUN
ajbmeb-2644	17	19	can	can	AUX
ajbmeb-2644	17	20	be	be	AUX
ajbmeb-2644	17	21	generated	generate	VERB
ajbmeb-2644	17	22	using	use	VERB
ajbmeb-2644	17	23	the	the	DET
ajbmeb-2644	17	24	exponential	exponential	ADJ
ajbmeb-2644	17	25	function	function	NOUN
ajbmeb-2644	17	26	properties	property	NOUN
ajbmeb-2644	17	27	.	.	PUNCT
ajbmeb-2644	18	1	in	in	ADP
ajbmeb-2644	18	2	particular	particular	ADJ
ajbmeb-2644	18	3	,	,	PUNCT
ajbmeb-2644	18	4	the	the	DET
ajbmeb-2644	18	5	defining	define	VERB
ajbmeb-2644	18	6	domain	domain	NOUN
ajbmeb-2644	18	7	of	of	ADP
ajbmeb-2644	18	8	the	the	DET
ajbmeb-2644	18	9	function	function	NOUN
ajbmeb-2644	18	10	f	f	PROPN
ajbmeb-2644	18	11	(	(	PUNCT
ajbmeb-2644	18	12	x	x	X
ajbmeb-2644	18	13	)	)	PUNCT
ajbmeb-2644	18	14	=	=	NOUN
ajbmeb-2644	18	15	ax	ax	NOUN
ajbmeb-2644	18	16	was	be	AUX
ajbmeb-2644	18	17	d(f	d(f	NOUN
ajbmeb-2644	18	18	)	)	PUNCT
ajbmeb-2644	19	1	=	=	SYM
ajbmeb-2644	19	2	{	{	PUNCT
ajbmeb-2644	19	3	-∞	-∞	PUNCT
ajbmeb-2644	19	4	<	<	X
ajbmeb-2644	19	5	x<+∞	x<+∞	PROPN
ajbmeb-2644	19	6	}	}	PUNCT
ajbmeb-2644	19	7	,	,	PUNCT
ajbmeb-2644	19	8	and	and	CCONJ
ajbmeb-2644	19	9	the	the	DET
ajbmeb-2644	19	10	domain	domain	NOUN
ajbmeb-2644	19	11	of	of	ADP
ajbmeb-2644	19	12	change	change	NOUN
ajbmeb-2644	19	13	was	be	AUX
ajbmeb-2644	19	14	e(f	e(f	PROPN
ajbmeb-2644	19	15	)	)	PUNCT
ajbmeb-2644	19	16	=	=	PUNCT
ajbmeb-2644	20	1	{	{	PUNCT
ajbmeb-2644	20	2	0	0	NUM
ajbmeb-2644	20	3	<	<	X
ajbmeb-2644	20	4	y<+∞	y<+∞	PROPN
ajbmeb-2644	20	5	}	}	PUNCT
ajbmeb-2644	20	6	.	.	PUNCT
ajbmeb-2644	21	1	accordingly	accordingly	ADV
ajbmeb-2644	21	2	,	,	PUNCT
ajbmeb-2644	21	3	for	for	ADP
ajbmeb-2644	21	4	a	a	DET
ajbmeb-2644	21	5	logax	logax	PROPN
ajbmeb-2644	21	6	function	function	NOUN
ajbmeb-2644	21	7	f(x	f(x	PROPN
ajbmeb-2644	21	8	)	)	PUNCT
ajbmeb-2644	21	9	=	=	SYM
ajbmeb-2644	21	10	d(f	d(f	NOUN
ajbmeb-2644	21	11	)	)	PUNCT
ajbmeb-2644	21	12	=	=	PUNCT
ajbmeb-2644	21	13	{	{	PUNCT
ajbmeb-2644	21	14	0	0	X
ajbmeb-2644	21	15	<	<	X
ajbmeb-2644	21	16	x<+∞	x<+∞	NUM
ajbmeb-2644	21	17	}	}	PUNCT
ajbmeb-2644	21	18	,	,	PUNCT
ajbmeb-2644	21	19	e(f	e(f	PROPN
ajbmeb-2644	21	20	)	)	PUNCT
ajbmeb-2644	21	21	=	=	PRON
ajbmeb-2644	21	22	{	{	PUNCT
ajbmeb-2644	21	23	-∞	-∞	PUNCT
ajbmeb-2644	21	24	<	<	X
ajbmeb-2644	21	25	y<+∞	y<+∞	PROPN
ajbmeb-2644	21	26	}	}	PUNCT
ajbmeb-2644	21	27	.	.	PUNCT
ajbmeb-2644	22	1	at	at	ADP
ajbmeb-2644	22	2	a	a	DET
ajbmeb-2644	22	3	>	>	X
ajbmeb-2644	22	4	1	1	NUM
ajbmeb-2644	22	5	,	,	PUNCT
ajbmeb-2644	22	6	the	the	DET
ajbmeb-2644	22	7	logax	logax	ADJ
ajbmeb-2644	22	8	function	function	NOUN
ajbmeb-2644	22	9	(	(	PUNCT
ajbmeb-2644	22	10	0	0	NUM
ajbmeb-2644	22	11	;	;	PUNCT
ajbmeb-2644	22	12	+	+	NOUN
ajbmeb-2644	22	13	∞	∞	NOUN
ajbmeb-2644	22	14	)	)	PUNCT
ajbmeb-2644	22	15	is	be	AUX
ajbmeb-2644	22	16	continuous	continuous	ADJ
ajbmeb-2644	22	17	in	in	ADP
ajbmeb-2644	22	18	light	light	NOUN
ajbmeb-2644	22	19	,	,	PUNCT
ajbmeb-2644	22	20	increasing	increase	VERB
ajbmeb-2644	22	21	,	,	PUNCT
ajbmeb-2644	22	22	negative	negative	ADJ
ajbmeb-2644	22	23	at	at	ADP
ajbmeb-2644	22	24	0	0	NUM
ajbmeb-2644	22	25	<	<	X
ajbmeb-2644	22	26	x	x	X
ajbmeb-2644	22	27	<	<	X
ajbmeb-2644	22	28	1	1	NUM
ajbmeb-2644	22	29	,	,	PUNCT
ajbmeb-2644	22	30	positive	positive	ADJ
ajbmeb-2644	22	31	at	at	ADP
ajbmeb-2644	22	32	x	x	X
ajbmeb-2644	22	33	>	>	X
ajbmeb-2644	22	34	1	1	NUM
ajbmeb-2644	22	35	,	,	PUNCT
ajbmeb-2644	22	36	increasing	increase	VERB
ajbmeb-2644	22	37	from	from	ADP
ajbmeb-2644	22	38	-∞	-∞	X
ajbmeb-2644	22	39	to+∞.	to+∞.	NOUN
ajbmeb-2644	22	40	similarly	similarly	ADV
ajbmeb-2644	22	41	at	at	ADP
ajbmeb-2644	22	42	0	0	NUM
ajbmeb-2644	22	43	<	<	X
ajbmeb-2644	22	44	a	a	DET
ajbmeb-2644	22	45	<	<	X
ajbmeb-2644	22	46	1	1	NUM
ajbmeb-2644	22	47	the	the	DET
ajbmeb-2644	22	48	function	function	NOUN
ajbmeb-2644	22	49	is	be	AUX
ajbmeb-2644	22	50	continuous	continuous	ADJ
ajbmeb-2644	22	51	at	at	ADP
ajbmeb-2644	22	52	(	(	PUNCT
ajbmeb-2644	22	53	0;+∞	0;+∞	NUM
ajbmeb-2644	22	54	)	)	PUNCT
ajbmeb-2644	22	55	,	,	PUNCT
ajbmeb-2644	22	56	decreasing	decrease	VERB
ajbmeb-2644	22	57	from	from	ADP
ajbmeb-2644	22	58	+	+	NOUN
ajbmeb-2644	22	59	∞	∞	NOUN
ajbmeb-2644	22	60	to	to	ADP
ajbmeb-2644	22	61	0	0	NUM
ajbmeb-2644	22	62	,	,	PUNCT
ajbmeb-2644	22	63	taking	take	VERB
ajbmeb-2644	22	64	positive	positive	ADJ
ajbmeb-2644	22	65	values	value	NOUN
ajbmeb-2644	22	66	at	at	ADP
ajbmeb-2644	22	67	0	0	NUM
ajbmeb-2644	22	68	<	<	X
ajbmeb-2644	22	69	x	x	X
ajbmeb-2644	22	70	<	<	X
ajbmeb-2644	22	71	1	1	NUM
ajbmeb-2644	22	72	range	range	NOUN
ajbmeb-2644	22	73	,	,	PUNCT
ajbmeb-2644	22	74	and	and	CCONJ
ajbmeb-2644	22	75	negative	negative	ADJ
ajbmeb-2644	22	76	values	value	NOUN
ajbmeb-2644	22	77	at	at	ADP
ajbmeb-2644	22	78	x	x	X
ajbmeb-2644	22	79	>	>	X
ajbmeb-2644	22	80	1	1	NUM
ajbmeb-2644	22	81	.	.	PUNCT
ajbmeb-2644	23	1	the	the	DET
ajbmeb-2644	23	2	ordinate	ordinate	NOUN
ajbmeb-2644	23	3	axis	axis	NOUN
ajbmeb-2644	23	4	is	be	AUX
ajbmeb-2644	23	5	a	a	DET
ajbmeb-2644	23	6	vertical	vertical	ADJ
ajbmeb-2644	23	7	asymptote	asymptote	NOUN
ajbmeb-2644	23	8	for	for	ADP
ajbmeb-2644	23	9	the	the	DET
ajbmeb-2644	23	10	logax	logax	ADJ
ajbmeb-2644	23	11	function	function	NOUN
ajbmeb-2644	23	12	.	.	PUNCT
ajbmeb-2644	24	1	american	american	ADJ
ajbmeb-2644	24	2	journal	journal	PROPN
ajbmeb-2644	24	3	of	of	ADP
ajbmeb-2644	24	4	business	business	NOUN
ajbmeb-2644	24	5	management	management	NOUN
ajbmeb-2644	24	6	,	,	PUNCT
ajbmeb-2644	24	7	economics	economic	NOUN
ajbmeb-2644	24	8	and	and	CCONJ
ajbmeb-2644	24	9	banking	banking	NOUN
ajbmeb-2644	24	10	volume	volume	NOUN
ajbmeb-2644	24	11	32	32	NUM
ajbmeb-2644	24	12	january	january	PROPN
ajbmeb-2644	24	13	2025	2025	NUM
ajbmeb-2644	24	14	p	p	NOUN
ajbmeb-2644	24	15	a	a	PRON
ajbmeb-2644	24	16	g	g	NOUN
ajbmeb-2644	24	17	e	e	NOUN
ajbmeb-2644	24	18	|	|	ADV
ajbmeb-2644	24	19	32	32	NUM
ajbmeb-2644	24	20	www.americanjournal.org	www.americanjournal.org	NOUN
ajbmeb-2644	24	21	let	let	VERB
ajbmeb-2644	24	22	's	us	PRON
ajbmeb-2644	24	23	consider	consider	VERB
ajbmeb-2644	24	24	the	the	DET
ajbmeb-2644	24	25	following	follow	VERB
ajbmeb-2644	24	26	examples	example	NOUN
ajbmeb-2644	24	27	:	:	PUNCT
ajbmeb-2644	24	28	1.to	1.to	NUM
ajbmeb-2644	24	29	solve	solve	VERB
ajbmeb-2644	24	30	2x=4	2x=4	NUM
ajbmeb-2644	24	31	,	,	PUNCT
ajbmeb-2644	24	32	we	we	PRON
ajbmeb-2644	24	33	write	write	VERB
ajbmeb-2644	24	34	2x=22	2x=22	NUM
ajbmeb-2644	24	35	and	and	CCONJ
ajbmeb-2644	24	36	find	find	VERB
ajbmeb-2644	24	37	the	the	DET
ajbmeb-2644	24	38	solution	solution	NOUN
ajbmeb-2644	24	39	x=2	x=2	PUNCT
ajbmeb-2644	24	40	.	.	PUNCT
ajbmeb-2644	25	1	2.let	2.let	ADP
ajbmeb-2644	25	2	2x	2x	NUM
ajbmeb-2644	25	3	=	=	SYM
ajbmeb-2644	25	4	5	5	X
ajbmeb-2644	25	5	.	.	PUNCT
ajbmeb-2644	26	1	it	it	PRON
ajbmeb-2644	26	2	is	be	AUX
ajbmeb-2644	26	3	difficult	difficult	ADJ
ajbmeb-2644	26	4	to	to	PART
ajbmeb-2644	26	5	describe	describe	VERB
ajbmeb-2644	26	6	5	5	NUM
ajbmeb-2644	26	7	on	on	ADP
ajbmeb-2644	26	8	the	the	DET
ajbmeb-2644	26	9	right	right	ADJ
ajbmeb-2644	26	10	side	side	NOUN
ajbmeb-2644	26	11	in	in	ADP
ajbmeb-2644	26	12	the	the	DET
ajbmeb-2644	26	13	form	form	NOUN
ajbmeb-2644	26	14	of	of	ADP
ajbmeb-2644	26	15	a	a	DET
ajbmeb-2644	26	16	degree	degree	NOUN
ajbmeb-2644	26	17	with	with	ADP
ajbmeb-2644	26	18	a	a	DET
ajbmeb-2644	26	19	base	base	NOUN
ajbmeb-2644	26	20	of	of	ADP
ajbmeb-2644	26	21	2	2	NUM
ajbmeb-2644	26	22	.	.	PUNCT
ajbmeb-2644	27	1	but	but	CCONJ
ajbmeb-2644	27	2	it	it	PRON
ajbmeb-2644	27	3	is	be	AUX
ajbmeb-2644	27	4	known	know	VERB
ajbmeb-2644	27	5	to	to	ADP
ajbmeb-2644	27	6	us	we	PRON
ajbmeb-2644	27	7	that	that	SCONJ
ajbmeb-2644	27	8	there	there	PRON
ajbmeb-2644	27	9	is	be	VERB
ajbmeb-2644	27	10	a	a	DET
ajbmeb-2644	27	11	real	real	ADJ
ajbmeb-2644	27	12	root	root	NOUN
ajbmeb-2644	27	13	of	of	ADP
ajbmeb-2644	27	14	this	this	DET
ajbmeb-2644	27	15	equation	equation	NOUN
ajbmeb-2644	27	16	.	.	PUNCT
ajbmeb-2644	28	1	to	to	PART
ajbmeb-2644	28	2	solve	solve	VERB
ajbmeb-2644	28	3	such	such	ADJ
ajbmeb-2644	28	4	equations	equation	NOUN
ajbmeb-2644	28	5	,	,	PUNCT
ajbmeb-2644	28	6	the	the	DET
ajbmeb-2644	28	7	concept	concept	NOUN
ajbmeb-2644	28	8	of	of	ADP
ajbmeb-2644	28	9	logarithm	logarithm	NOUN
ajbmeb-2644	28	10	is	be	AUX
ajbmeb-2644	28	11	introduced	introduce	VERB
ajbmeb-2644	28	12	.	.	PUNCT
ajbmeb-2644	29	1	in	in	ADP
ajbmeb-2644	29	2	general	general	ADJ
ajbmeb-2644	29	3	,	,	PUNCT
ajbmeb-2644	29	4	the	the	DET
ajbmeb-2644	29	5	root	root	NOUN
ajbmeb-2644	29	6	of	of	ADP
ajbmeb-2644	29	7	the	the	DET
ajbmeb-2644	29	8	equation	equation	NOUN
ajbmeb-2644	29	9	ax	ax	NOUN
ajbmeb-2644	29	10	=	=	SYM
ajbmeb-2644	29	11	b	b	PROPN
ajbmeb-2644	29	12	(	(	PUNCT
ajbmeb-2644	29	13	a>0	a>0	PROPN
ajbmeb-2644	29	14	,	,	PUNCT
ajbmeb-2644	29	15	a≠1	a≠1	ADJ
ajbmeb-2644	29	16	,	,	PUNCT
ajbmeb-2644	29	17	b>0	b>0	NOUN
ajbmeb-2644	29	18	)	)	PUNCT
ajbmeb-2644	29	19	is	be	AUX
ajbmeb-2644	29	20	called	call	VERB
ajbmeb-2644	29	21	the	the	DET
ajbmeb-2644	29	22	logarithm	logarithm	NOUN
ajbmeb-2644	29	23	of	of	ADP
ajbmeb-2644	29	24	the	the	DET
ajbmeb-2644	29	25	number	number	NOUN
ajbmeb-2644	29	26	b	b	NOUN
ajbmeb-2644	29	27	according	accord	VERB
ajbmeb-2644	29	28	to	to	ADP
ajbmeb-2644	29	29	base	base	NOUN
ajbmeb-2644	29	30	a.	a.	NOUN
ajbmeb-2644	29	31	description	description	NOUN
ajbmeb-2644	29	32	:	:	PUNCT
ajbmeb-2644	29	33	the	the	DET
ajbmeb-2644	29	34	logarithm	logarithm	NOUN
ajbmeb-2644	29	35	of	of	ADP
ajbmeb-2644	29	36	a	a	DET
ajbmeb-2644	29	37	number	number	NOUN
ajbmeb-2644	29	38	b	b	NOUN
ajbmeb-2644	29	39	according	accord	VERB
ajbmeb-2644	29	40	to	to	ADP
ajbmeb-2644	29	41	base	base	NOUN
ajbmeb-2644	29	42	a	a	PRON
ajbmeb-2644	29	43	is	be	AUX
ajbmeb-2644	29	44	said	say	VERB
ajbmeb-2644	29	45	to	to	PART
ajbmeb-2644	29	46	be	be	AUX
ajbmeb-2644	29	47	the	the	DET
ajbmeb-2644	29	48	degree	degree	NOUN
ajbmeb-2644	29	49	indicator	indicator	NOUN
ajbmeb-2644	29	50	that	that	SCONJ
ajbmeb-2644	29	51	a	a	DET
ajbmeb-2644	29	52	number	number	NOUN
ajbmeb-2644	29	53	will	will	AUX
ajbmeb-2644	29	54	need	need	VERB
ajbmeb-2644	29	55	to	to	PART
ajbmeb-2644	29	56	be	be	AUX
ajbmeb-2644	29	57	raised	raise	VERB
ajbmeb-2644	29	58	to	to	PART
ajbmeb-2644	29	59	form	form	VERB
ajbmeb-2644	29	60	a	a	DET
ajbmeb-2644	29	61	number	number	NOUN
ajbmeb-2644	29	62	b	b	NOUN
ajbmeb-2644	29	63	,	,	PUNCT
ajbmeb-2644	29	64	and	and	CCONJ
ajbmeb-2644	29	65	is	be	AUX
ajbmeb-2644	29	66	defined	define	VERB
ajbmeb-2644	29	67	as	as	ADP
ajbmeb-2644	29	68	logab	logab	NOUN
ajbmeb-2644	29	69	.	.	PUNCT
ajbmeb-2644	30	1	ax	ax	NOUN
ajbmeb-2644	30	2	=	=	NOUN
ajbmeb-2644	30	3	equation	equation	NOUN
ajbmeb-2644	30	4	b	b	X
ajbmeb-2644	30	5	(	(	PUNCT
ajbmeb-2644	30	6	since	since	SCONJ
ajbmeb-2644	30	7	x	x	NOUN
ajbmeb-2644	30	8	=	=	NOUN
ajbmeb-2644	30	9	logab	logab	ADJ
ajbmeb-2644	30	10	aloga	aloga	NOUN
ajbmeb-2644	30	11	b	b	PROPN
ajbmeb-2644	30	12	/	/	SYM
ajbmeb-2644	30	13	b	b	PROPN
ajbmeb-2644	30	14	(	(	PUNCT
ajbmeb-2644	30	15	1	1	NUM
ajbmeb-2644	30	16	)	)	PUNCT
ajbmeb-2644	30	17	<	<	X
ajbmeb-2644	30	18	br	br	X
ajbmeb-2644	30	19	>	>	X
ajbmeb-2644	30	20	can	can	AUX
ajbmeb-2644	30	21	be	be	AUX
ajbmeb-2644	30	22	written	write	VERB
ajbmeb-2644	30	23	in	in	ADP
ajbmeb-2644	30	24	the	the	DET
ajbmeb-2644	30	25	form	form	NOUN
ajbmeb-2644	30	26	.	.	PUNCT
ajbmeb-2644	31	1	(	(	PUNCT
ajbmeb-2644	31	2	1	1	X
ajbmeb-2644	31	3	)	)	PUNCT
ajbmeb-2644	31	4	the	the	DET
ajbmeb-2644	31	5	formula	formula	NOUN
ajbmeb-2644	31	6	is	be	AUX
ajbmeb-2644	31	7	called	call	VERB
ajbmeb-2644	31	8	the	the	DET
ajbmeb-2644	31	9	basic	basic	ADJ
ajbmeb-2644	31	10	logarithmic	logarithmic	ADJ
ajbmeb-2644	31	11	axiom	axiom	NOUN
ajbmeb-2644	31	12	,	,	PUNCT
ajbmeb-2644	31	13	where	where	SCONJ
ajbmeb-2644	31	14	a>0a≠1vab>0	a>0a≠1vab>0	ADV
ajbmeb-2644	31	15	2	2	X
ajbmeb-2644	31	16	)	)	PUNCT
ajbmeb-2644	31	17	examples	example	NOUN
ajbmeb-2644	31	18	:	:	PUNCT
ajbmeb-2644	31	19	1	1	NUM
ajbmeb-2644	31	20	)	)	PUNCT
ajbmeb-2644	31	21	log2162	log2162	NOUN
ajbmeb-2644	31	22	)	)	PUNCT
ajbmeb-2644	31	23	find	find	VERB
ajbmeb-2644	31	24	the	the	DET
ajbmeb-2644	31	25	value	value	NOUN
ajbmeb-2644	31	26	of	of	ADP
ajbmeb-2644	31	27	log50,04	log50,04	PROPN
ajbmeb-2644	31	28	.	.	NOUN
ajbmeb-2644	31	29	3	3	X
ajbmeb-2644	31	30	)	)	PUNCT
ajbmeb-2644	31	31	solution	solution	NOUN
ajbmeb-2644	31	32	:	:	PUNCT
ajbmeb-2644	31	33	1	1	X
ajbmeb-2644	31	34	)	)	PUNCT
ajbmeb-2644	31	35	since	since	SCONJ
ajbmeb-2644	31	36	16=24	16=24	NUM
ajbmeb-2644	31	37	,	,	PUNCT
ajbmeb-2644	31	38	it	it	PRON
ajbmeb-2644	31	39	is	be	AUX
ajbmeb-2644	31	40	necessary	necessary	ADJ
ajbmeb-2644	31	41	to	to	PART
ajbmeb-2644	31	42	raise	raise	VERB
ajbmeb-2644	31	43	the	the	DET
ajbmeb-2644	31	44	two	two	NUM
ajbmeb-2644	31	45	to	to	ADP
ajbmeb-2644	31	46	the	the	DET
ajbmeb-2644	31	47	fourth	fourth	ADJ
ajbmeb-2644	31	48	level	level	NOUN
ajbmeb-2644	31	49	to	to	PART
ajbmeb-2644	31	50	form	form	VERB
ajbmeb-2644	31	51	16	16	NUM
ajbmeb-2644	31	52	,	,	PUNCT
ajbmeb-2644	31	53	which	which	PRON
ajbmeb-2644	31	54	means	mean	VERB
ajbmeb-2644	31	55	log216	log216	ADJ
ajbmeb-2644	31	56	=	=	SYM
ajbmeb-2644	31	57	4	4	NUM
ajbmeb-2644	31	58	.	.	NOUN
ajbmeb-2644	31	59	4	4	NUM
ajbmeb-2644	31	60	)	)	PUNCT
ajbmeb-2644	31	61	2)it	2)it	PROPN
ajbmeb-2644	31	62	is	be	AUX
ajbmeb-2644	31	63	known	know	VERB
ajbmeb-2644	31	64	that	that	SCONJ
ajbmeb-2644	31	65	0,04	0,04	NUM
ajbmeb-2644	31	66	%	%	NOUN
ajbmeb-2644	31	67	of	of	ADP
ajbmeb-2644	31	68	the	the	DET
ajbmeb-2644	31	69	volume	volume	NOUN
ajbmeb-2644	31	70	is	be	AUX
ajbmeb-2644	31	71	5	5	NUM
ajbmeb-2644	31	72	%	%	NOUN
ajbmeb-2644	31	73	.	.	PUNCT
ajbmeb-2644	32	1	therefore	therefore	ADV
ajbmeb-2644	32	2	log50	log50	ADV
ajbmeb-2644	32	3	,	,	PUNCT
ajbmeb-2644	32	4	04=-2	04=-2	NUM
ajbmeb-2644	32	5	5	5	NUM
ajbmeb-2644	32	6	)	)	PUNCT
ajbmeb-2644	32	7	examples	example	NOUN
ajbmeb-2644	32	8	:	:	PUNCT
ajbmeb-2644	32	9	3	3	X
ajbmeb-2644	32	10	.	.	X
ajbmeb-2644	32	11	we	we	PRON
ajbmeb-2644	32	12	find	find	VERB
ajbmeb-2644	32	13	log4	log4	NOUN
ajbmeb-2644	32	14	x	x	PART
ajbmeb-2644	32	15	to	to	PART
ajbmeb-2644	32	16	satisfy	satisfy	VERB
ajbmeb-2644	32	17	the	the	DET
ajbmeb-2644	32	18	equations	equation	NOUN
ajbmeb-2644	32	19	4	4	NUM
ajbmeb-2644	32	20	)	)	PUNCT
ajbmeb-2644	32	21	log	log	NOUN
ajbmeb-2644	32	22	x	x	SYM
ajbmeb-2644	32	23	4	4	NUM
ajbmeb-2644	32	24	to	to	PART
ajbmeb-2644	32	25	satisfy	satisfy	VERB
ajbmeb-2644	32	26	.	.	PUNCT
ajbmeb-2644	33	1	6	6	NUM
ajbmeb-2644	33	2	)	)	PUNCT
ajbmeb-2644	33	3	solution	solution	NOUN
ajbmeb-2644	33	4	:	:	PUNCT
ajbmeb-2644	33	5	using	use	VERB
ajbmeb-2644	33	6	the	the	DET
ajbmeb-2644	33	7	basic	basic	ADJ
ajbmeb-2644	33	8	logarithmic	logarithmic	ADJ
ajbmeb-2644	33	9	axiom	axiom	NOUN
ajbmeb-2644	33	10	:	:	PUNCT
ajbmeb-2644	33	11	7	7	NUM
ajbmeb-2644	33	12	)	)	PUNCT
ajbmeb-2644	33	13	8)	8)	NUM
ajbmeb-2644	33	14	xlogx	xlogx	PROPN
ajbmeb-2644	33	15	4	4	NUM
ajbmeb-2644	33	16	4	4	NUM
ajbmeb-2644	33	17	,	,	PUNCT
ajbmeb-2644	33	18	ya`ni	ya`ni	NOUN
ajbmeb-2644	33	19	x	x	SYM
ajbmeb-2644	33	20	34	34	NUM
ajbmeb-2644	33	21	4	4	NUM
ajbmeb-2644	33	22	,	,	PUNCT
ajbmeb-2644	33	23	x	x	PROPN
ajbmeb-2644	33	24	4	4	NUM
ajbmeb-2644	33	25	34	34	NUM
ajbmeb-2644	33	26	1	1	NUM
ajbmeb-2644	33	27	we	we	PRON
ajbmeb-2644	33	28	find	find	VERB
ajbmeb-2644	33	29	the	the	DET
ajbmeb-2644	33	30	s.	s.	PROPN
ajbmeb-2644	33	31	9	9	NUM
ajbmeb-2644	33	32	)	)	PUNCT
ajbmeb-2644	33	33	3	3	NUM
ajbmeb-2644	33	34	256	256	NUM
ajbmeb-2644	33	35	for	for	ADP
ajbmeb-2644	33	36	any	any	DET
ajbmeb-2644	33	37	number	number	NOUN
ajbmeb-2644	33	38	a>0	a>0	NOUN
ajbmeb-2644	33	39	,	,	PUNCT
ajbmeb-2644	33	40	b>0	b>0	PRON
ajbmeb-2644	33	41	,	,	PUNCT
ajbmeb-2644	33	42	a	a	DET
ajbmeb-2644	33	43	1	1	NUM
ajbmeb-2644	33	44	1	1	NUM
ajbmeb-2644	33	45	,	,	PUNCT
ajbmeb-2644	33	46	b	b	PROPN
ajbmeb-2644	33	47	1	1	NUM
ajbmeb-2644	33	48	1	1	NUM
ajbmeb-2644	33	49	,	,	PUNCT
ajbmeb-2644	33	50	x>0	x>0	NOUN
ajbmeb-2644	33	51	,	,	PUNCT
ajbmeb-2644	33	52	y>0	y>0	NOUN
ajbmeb-2644	33	53	,	,	PUNCT
ajbmeb-2644	33	54	and	and	CCONJ
ajbmeb-2644	33	55	the	the	DET
ajbmeb-2644	33	56	real	real	ADV
ajbmeb-2644	33	57	desired	desire	VERB
ajbmeb-2644	33	58	numbers	number	NOUN
ajbmeb-2644	33	59	n	n	PRON
ajbmeb-2644	33	60	and	and	CCONJ
ajbmeb-2644	33	61	m	m	PROPN
ajbmeb-2644	33	62	,	,	PUNCT
ajbmeb-2644	33	63	the	the	DET
ajbmeb-2644	33	64	following	follow	VERB
ajbmeb-2644	33	65	equalities	equality	NOUN
ajbmeb-2644	33	66	are	be	AUX
ajbmeb-2644	33	67	satisfied	satisfied	ADJ
ajbmeb-2644	33	68	:	:	PUNCT
ajbmeb-2644	33	69	1	1	X
ajbmeb-2644	33	70	)	)	PUNCT
ajbmeb-2644	33	71	log	log	VERB
ajbmeb-2644	33	72	a	a	DET
ajbmeb-2644	33	73	1	1	NUM
ajbmeb-2644	33	74	0	0	NUM
ajbmeb-2644	33	75	,	,	PUNCT
ajbmeb-2644	33	76	2	2	X
ajbmeb-2644	33	77	)	)	PUNCT
ajbmeb-2644	33	78	log	log	VERB
ajbmeb-2644	33	79	a	a	DET
ajbmeb-2644	33	80	a	a	DET
ajbmeb-2644	33	81	1	1	NUM
ajbmeb-2644	33	82	,	,	PUNCT
ajbmeb-2644	33	83	3	3	X
ajbmeb-2644	33	84	)	)	PUNCT
ajbmeb-2644	33	85	log	log	VERB
ajbmeb-2644	33	86	a	a	DET
ajbmeb-2644	33	87	(	(	PUNCT
ajbmeb-2644	33	88	xy	xy	NOUN
ajbmeb-2644	33	89	)	)	PUNCT
ajbmeb-2644	33	90	log	log	VERB
ajbmeb-2644	33	91	a	a	DET
ajbmeb-2644	33	92	x	x	NOUN
ajbmeb-2644	33	93	log	log	VERB
ajbmeb-2644	33	94	a	a	DET
ajbmeb-2644	33	95	y	y	NOUN
ajbmeb-2644	33	96	,	,	PUNCT
ajbmeb-2644	33	97	x	x	NOUN
ajbmeb-2644	33	98	4	4	X
ajbmeb-2644	33	99	)	)	PUNCT
ajbmeb-2644	33	100	log	log	VERB
ajbmeb-2644	33	101	a	a	DET
ajbmeb-2644	33	102	log	log	NOUN
ajbmeb-2644	34	1	a	a	DET
ajbmeb-2644	34	2	x	x	NOUN
ajbmeb-2644	34	3	log	log	VERB
ajbmeb-2644	34	4	a	a	DET
ajbmeb-2644	34	5	y	y	PROPN
ajbmeb-2644	34	6	,	,	PUNCT
ajbmeb-2644	34	7	y	y	PROPN
ajbmeb-2644	34	8	5	5	NUM
ajbmeb-2644	34	9	)	)	PUNCT
ajbmeb-2644	34	10	log	log	VERB
ajbmeb-2644	34	11	a	a	DET
ajbmeb-2644	34	12	x	x	NOUN
ajbmeb-2644	34	13	n	n	NUM
ajbmeb-2644	34	14	nlog	nlog	NOUN
ajbmeb-2644	34	15	a	a	DET
ajbmeb-2644	34	16	x	x	NOUN
ajbmeb-2644	34	17	,	,	PUNCT
ajbmeb-2644	34	18	1	1	NUM
ajbmeb-2644	34	19	6	6	NUM
ajbmeb-2644	34	20	)	)	PUNCT
ajbmeb-2644	34	21	log	log	NOUN
ajbmeb-2644	34	22	am	be	AUX
ajbmeb-2644	34	23	x	x	PART
ajbmeb-2644	34	24	m	m	VERB
ajbmeb-2644	34	25	log	log	VERB
ajbmeb-2644	34	26	a	a	DET
ajbmeb-2644	34	27	x	x	NOUN
ajbmeb-2644	34	28	,	,	PUNCT
ajbmeb-2644	34	29	7	7	X
ajbmeb-2644	34	30	)	)	PUNCT
ajbmeb-2644	34	31	log	log	NOUN
ajbmeb-2644	34	32	am	be	AUX
ajbmeb-2644	34	33	xn	xn	PROPN
ajbmeb-2644	34	34	mn	mn	PROPN
ajbmeb-2644	34	35	log	log	VERB
ajbmeb-2644	34	36	a	a	DET
ajbmeb-2644	34	37	x	x	NOUN
ajbmeb-2644	34	38	,	,	PUNCT
ajbmeb-2644	34	39	logb	logb	NOUN
ajbmeb-2644	34	40	x	x	SYM
ajbmeb-2644	34	41	,	,	PUNCT
ajbmeb-2644	34	42	8)	8)	NUM
ajbmeb-2644	34	43	log	log	VERB
ajbmeb-2644	34	44	a	a	DET
ajbmeb-2644	34	45	x	x	X
ajbmeb-2644	34	46	logb	logb	NOUN
ajbmeb-2644	34	47	a	a	DET
ajbmeb-2644	34	48	1	1	NUM
ajbmeb-2644	34	49	9	9	NUM
ajbmeb-2644	34	50	)	)	PUNCT
ajbmeb-2644	34	51	log	log	VERB
ajbmeb-2644	34	52	a	a	DET
ajbmeb-2644	34	53	b	b	NOUN
ajbmeb-2644	34	54	,	,	PUNCT
ajbmeb-2644	34	55	logb	logb	VERB
ajbmeb-2644	34	56	a	a	DET
ajbmeb-2644	34	57	these	these	DET
ajbmeb-2644	34	58	equalities	equality	NOUN
ajbmeb-2644	34	59	arise	arise	VERB
ajbmeb-2644	34	60	from	from	ADP
ajbmeb-2644	34	61	the	the	DET
ajbmeb-2644	34	62	properties	property	NOUN
ajbmeb-2644	34	63	of	of	ADP
ajbmeb-2644	34	64	the	the	DET
ajbmeb-2644	34	65	exponential	exponential	ADJ
ajbmeb-2644	34	66	function	function	NOUN
ajbmeb-2644	34	67	.	.	PUNCT
ajbmeb-2644	35	1	we	we	PRON
ajbmeb-2644	35	2	will	will	AUX
ajbmeb-2644	35	3	prove	prove	VERB
ajbmeb-2644	35	4	some	some	PRON
ajbmeb-2644	35	5	of	of	ADP
ajbmeb-2644	35	6	these	these	PRON
ajbmeb-2644	35	7	.	.	PUNCT
ajbmeb-2644	36	1	using	use	VERB
ajbmeb-2644	36	2	logarithmic	logarithmic	ADJ
ajbmeb-2644	36	3	axiom	axiom	NOUN
ajbmeb-2644	36	4	:	:	PUNCT
ajbmeb-2644	36	5	x	x	PART
ajbmeb-2644	36	6	aloga	aloga	NOUN
ajbmeb-2644	36	7	x	x	NOUN
ajbmeb-2644	36	8	,	,	PUNCT
ajbmeb-2644	36	9	y	y	PROPN
ajbmeb-2644	36	10	aloga	aloga	NOUN
ajbmeb-2644	36	11	y	y	PROPN
ajbmeb-2644	36	12	we	we	PRON
ajbmeb-2644	36	13	find	find	VERB
ajbmeb-2644	36	14	the	the	DET
ajbmeb-2644	36	15	.	.	PUNCT
ajbmeb-2644	36	16	american	american	PROPN
ajbmeb-2644	36	17	journal	journal	PROPN
ajbmeb-2644	36	18	of	of	ADP
ajbmeb-2644	36	19	business	business	NOUN
ajbmeb-2644	36	20	management	management	NOUN
ajbmeb-2644	36	21	,	,	PUNCT
ajbmeb-2644	36	22	economics	economic	NOUN
ajbmeb-2644	36	23	and	and	CCONJ
ajbmeb-2644	36	24	banking	banking	NOUN
ajbmeb-2644	36	25	volume	volume	NOUN
ajbmeb-2644	36	26	32	32	NUM
ajbmeb-2644	36	27	january	january	PROPN
ajbmeb-2644	36	28	2025	2025	NUM
ajbmeb-2644	36	29	p	p	NOUN
ajbmeb-2644	36	30	a	a	DET
ajbmeb-2644	36	31	g	g	NOUN
ajbmeb-2644	36	32	e	e	NOUN
ajbmeb-2644	36	33	|	|	ADV
ajbmeb-2644	36	34	33	33	NUM
ajbmeb-2644	36	35	www.americanjournal.org	www.americanjournal.org	NOUN
ajbmeb-2644	36	36	whether	whether	SCONJ
ajbmeb-2644	36	37	or	or	CCONJ
ajbmeb-2644	36	38	not	not	PART
ajbmeb-2644	36	39	we	we	PRON
ajbmeb-2644	36	40	multiply	multiply	VERB
ajbmeb-2644	36	41	these	these	DET
ajbmeb-2644	36	42	equalities	equality	NOUN
ajbmeb-2644	36	43	by	by	ADP
ajbmeb-2644	36	44	terms	term	NOUN
ajbmeb-2644	36	45	xy	xy	ADP
ajbmeb-2644	36	46	aloga	aloga	NOUN
ajbmeb-2644	36	47	x	x	PUNCT
ajbmeb-2644	36	48	*	*	PUNCT
ajbmeb-2644	36	49	aloga	aloga	NOUN
ajbmeb-2644	36	50	y	y	PROPN
ajbmeb-2644	36	51	aloga	aloga	NOUN
ajbmeb-2644	36	52	x	x	PROPN
ajbmeb-2644	36	53	loga	loga	PROPN
ajbmeb-2644	36	54	y	y	PROPN
ajbmeb-2644	36	55	,	,	PUNCT
ajbmeb-2644	36	56	x	x	PART
ajbmeb-2644	36	57	aloga	aloga	NOUN
ajbmeb-2644	36	58	x	x	NOUN
ajbmeb-2644	36	59	:	:	PUNCT
ajbmeb-2644	36	60	aloga	aloga	NOUN
ajbmeb-2644	36	61	y	y	PROPN
ajbmeb-2644	36	62	aloga	aloga	PROPN
ajbmeb-2644	36	63	x	x	PROPN
ajbmeb-2644	36	64	loga	loga	PROPN
ajbmeb-2644	36	65	y	y	PROPN
ajbmeb-2644	36	66	,	,	PUNCT
ajbmeb-2644	36	67	is	be	AUX
ajbmeb-2644	36	68	formed	form	VERB
ajbmeb-2644	36	69	.	.	PUNCT
ajbmeb-2644	37	1	y	y	PROPN
ajbmeb-2644	37	2	from	from	ADP
ajbmeb-2644	37	3	these	these	DET
ajbmeb-2644	37	4	equalities	equality	NOUN
ajbmeb-2644	37	5	come	come	VERB
ajbmeb-2644	37	6	the	the	DET
ajbmeb-2644	37	7	equalities	equality	NOUN
ajbmeb-2644	37	8	3	3	NUM
ajbmeb-2644	37	9	)	)	PUNCT
ajbmeb-2644	37	10	and	and	CCONJ
ajbmeb-2644	37	11	4	4	NUM
ajbmeb-2644	37	12	)	)	PUNCT
ajbmeb-2644	37	13	according	accord	VERB
ajbmeb-2644	37	14	to	to	ADP
ajbmeb-2644	37	15	the	the	DET
ajbmeb-2644	37	16	definition	definition	NOUN
ajbmeb-2644	37	17	of	of	ADP
ajbmeb-2644	37	18	the	the	DET
ajbmeb-2644	37	19	logarithm	logarithm	NOUN
ajbmeb-2644	37	20	.	.	PUNCT
ajbmeb-2644	38	1	x	x	PUNCT
ajbmeb-2644	38	2	to	to	ADP
ajbmeb-2644	38	3	alo	alo	NOUN
ajbmeb-2644	38	4	x	x	PUNCT
ajbmeb-2644	38	5	if	if	SCONJ
ajbmeb-2644	38	6	we	we	PRON
ajbmeb-2644	38	7	increase	increase	VERB
ajbmeb-2644	38	8	both	both	DET
ajbmeb-2644	38	9	sides	side	NOUN
ajbmeb-2644	38	10	of	of	ADP
ajbmeb-2644	38	11	the	the	DET
ajbmeb-2644	38	12	mirror	mirror	NOUN
ajbmeb-2644	38	13	to	to	ADP
ajbmeb-2644	38	14	n	n	CCONJ
ajbmeb-2644	38	15	-	-	PUNCT
ajbmeb-2644	38	16	level	level	NOUN
ajbmeb-2644	38	17	,	,	PUNCT
ajbmeb-2644	38	18	x	x	PUNCT
ajbmeb-2644	38	19	to	to	ADP
ajbmeb-2644	38	20	alo	alo	NOUN
ajbmeb-2644	38	21	x	x	PUNCT
ajbmeb-2644	38	22	yields	yield	NOUN
ajbmeb-2644	38	23	and	and	CCONJ
ajbmeb-2644	38	24	from	from	ADP
ajbmeb-2644	38	25	this	this	PRON
ajbmeb-2644	38	26	we	we	PRON
ajbmeb-2644	38	27	find	find	VERB
ajbmeb-2644	38	28	loga	loga	NOUN
ajbmeb-2644	38	29	x	x	PUNCT
ajbmeb-2644	38	30	to	to	ADP
ajbmeb-2644	38	31	nlo	nlo	PROPN
ajbmeb-2644	38	32	.	.	PUNCT
ajbmeb-2644	39	1	to	to	PART
ajbmeb-2644	39	2	prove	prove	VERB
ajbmeb-2644	39	3	that	that	SCONJ
ajbmeb-2644	39	4	the	the	DET
ajbmeb-2644	39	5	formula	formula	NOUN
ajbmeb-2644	39	6	for	for	ADP
ajbmeb-2644	39	7	the	the	DET
ajbmeb-2644	39	8	transition	transition	NOUN
ajbmeb-2644	39	9	from	from	ADP
ajbmeb-2644	39	10	one	one	NUM
ajbmeb-2644	39	11	-	-	PUNCT
ajbmeb-2644	39	12	base	base	NOUN
ajbmeb-2644	39	13	logarithm	logarithm	NOUN
ajbmeb-2644	39	14	to	to	ADP
ajbmeb-2644	39	15	another	another	DET
ajbmeb-2644	39	16	-	-	PUNCT
ajbmeb-2644	39	17	base	base	NOUN
ajbmeb-2644	39	18	logarithm	logarithm	NOUN
ajbmeb-2644	39	19	is	be	AUX
ajbmeb-2644	39	20	8)	8)	NUM
ajbmeb-2644	39	21	in	in	ADP
ajbmeb-2644	39	22	private	private	ADJ
ajbmeb-2644	39	23	9	9	NUM
ajbmeb-2644	39	24	)	)	PUNCT
ajbmeb-2644	39	25	,	,	PUNCT
ajbmeb-2644	39	26	we	we	PRON
ajbmeb-2644	39	27	proceed	proceed	VERB
ajbmeb-2644	39	28	as	as	SCONJ
ajbmeb-2644	39	29	follows	follow	VERB
ajbmeb-2644	39	30	:	:	PUNCT
ajbmeb-2644	39	31	loga	loga	NOUN
ajbmeb-2644	39	32	x	x	SYM
ajbmeb-2644	39	33	gömək	gömək	PROPN
ajbmeb-2644	39	34	b	b	PROPN
ajbmeb-2644	39	35	gömək	gömək	NOUN
ajbmeb-2644	39	36	from	from	ADP
ajbmeb-2644	39	37	both	both	DET
ajbmeb-2644	39	38	sides	side	NOUN
ajbmeb-2644	39	39	of	of	ADP
ajbmeb-2644	39	40	the	the	DET
ajbmeb-2644	39	41	resulting	result	VERB
ajbmeb-2644	39	42	expression	expression	NOUN
ajbmeb-2644	39	43	x	x	X
ajbmeb-2644	39	44	=	=	X
ajbmeb-2644	39	45	ab	ab	X
ajbmeb-2644	39	46	we	we	PRON
ajbmeb-2644	39	47	find	find	VERB
ajbmeb-2644	39	48	a	a	DET
ajbmeb-2644	39	49	logarithm	logarithm	NOUN
ajbmeb-2644	39	50	according	accord	VERB
ajbmeb-2644	39	51	to	to	ADP
ajbmeb-2644	39	52	base	base	NOUN
ajbmeb-2644	39	53	b	b	NOUN
ajbmeb-2644	39	54	:	:	PUNCT
ajbmeb-2644	39	55	b	b	X
ajbmeb-2644	39	56	blogb	blogb	NOUN
ajbmeb-2644	39	57	a	a	DET
ajbmeb-2644	39	58	b	b	NOUN
ajbmeb-2644	39	59	logb	logb	NOUN
ajbmeb-2644	39	60	x	x	INTJ
ajbmeb-2644	39	61	logb	logb	ADV
ajbmeb-2644	39	62	x	x	INTJ
ajbmeb-2644	39	63	logb	logb	VERB
ajbmeb-2644	39	64	a	a	DET
ajbmeb-2644	39	65	logb	logb	NOUN
ajbmeb-2644	39	66	a	a	DET
ajbmeb-2644	39	67	putting	put	VERB
ajbmeb-2644	39	68	the	the	DET
ajbmeb-2644	39	69	value	value	NOUN
ajbmeb-2644	39	70	of	of	ADP
ajbmeb-2644	39	71	b	b	NOUN
ajbmeb-2644	39	72	on	on	ADP
ajbmeb-2644	39	73	the	the	DET
ajbmeb-2644	39	74	left	left	ADJ
ajbmeb-2644	39	75	side	side	NOUN
ajbmeb-2644	39	76	,	,	PUNCT
ajbmeb-2644	39	77	we	we	PRON
ajbmeb-2644	39	78	obtain	obtain	VERB
ajbmeb-2644	39	79	the	the	DET
ajbmeb-2644	39	80	formula	formula	NOUN
ajbmeb-2644	39	81	8)	8)	NUM
ajbmeb-2644	39	82	.	.	PUNCT
ajbmeb-2644	40	1	if	if	SCONJ
ajbmeb-2644	40	2	we	we	PRON
ajbmeb-2644	40	3	say	say	VERB
ajbmeb-2644	40	4	x	x	X
ajbmeb-2644	40	5	=	=	NOUN
ajbmeb-2644	40	6	b	b	X
ajbmeb-2644	40	7	from	from	ADP
ajbmeb-2644	40	8	this	this	DET
ajbmeb-2644	40	9	formula	formula	NOUN
ajbmeb-2644	40	10	,	,	PUNCT
ajbmeb-2644	40	11	we	we	PRON
ajbmeb-2644	40	12	get	get	VERB
ajbmeb-2644	40	13	the	the	DET
ajbmeb-2644	40	14	formula	formula	NOUN
ajbmeb-2644	40	15	9	9	NUM
ajbmeb-2644	40	16	)	)	PUNCT
ajbmeb-2644	40	17	.	.	PUNCT
ajbmeb-2644	41	1	5example	5example	NUM
ajbmeb-2644	41	2	.	.	PUNCT
ajbmeb-2644	42	1	if	if	SCONJ
ajbmeb-2644	42	2	log25	log25	VERB
ajbmeb-2644	42	3	a	a	DET
ajbmeb-2644	42	4	va	va	NOUN
ajbmeb-2644	42	5	log23	log23	PROPN
ajbmeb-2644	42	6	b	b	PROPN
ajbmeb-2644	42	7	bo`lsa	bo`lsa	NOUN
ajbmeb-2644	42	8	,	,	PUNCT
ajbmeb-2644	42	9	log23000	log23000	NOUN
ajbmeb-2644	42	10	ni	ni	PROPN
ajbmeb-2644	42	11	a	a	DET
ajbmeb-2644	42	12	va	va	PROPN
ajbmeb-2644	42	13	b	b	AUX
ajbmeb-2644	42	14	express	express	VERB
ajbmeb-2644	42	15	through	through	ADP
ajbmeb-2644	42	16	?	?	PUNCT
ajbmeb-2644	43	1	solution	solution	NOUN
ajbmeb-2644	43	2	:	:	PUNCT
ajbmeb-2644	43	3	log	log	NOUN
ajbmeb-2644	43	4	2	2	NUM
ajbmeb-2644	43	5	3000	3000	NUM
ajbmeb-2644	43	6	log	log	NOUN
ajbmeb-2644	43	7	2	2	NUM
ajbmeb-2644	43	8	(	(	PUNCT
ajbmeb-2644	43	9	3	3	NUM
ajbmeb-2644	43	10	53	53	NUM
ajbmeb-2644	43	11	23	23	NUM
ajbmeb-2644	43	12	)	)	PUNCT
ajbmeb-2644	43	13	log	log	VERB
ajbmeb-2644	43	14	2	2	NUM
ajbmeb-2644	43	15	3	3	NUM
ajbmeb-2644	43	16	3log	3log	NUM
ajbmeb-2644	43	17	2	2	NUM
ajbmeb-2644	43	18	5	5	NUM
ajbmeb-2644	43	19	3log	3log	NUM
ajbmeb-2644	43	20	2	2	NUM
ajbmeb-2644	43	21	2	2	NUM
ajbmeb-2644	43	22	b	b	PROPN
ajbmeb-2644	43	23	3a	3a	NUM
ajbmeb-2644	43	24	3	3	NUM
ajbmeb-2644	43	25	6	6	NUM
ajbmeb-2644	43	26	-	-	PUNCT
ajbmeb-2644	43	27	xample	xample	NOUN
ajbmeb-2644	43	28	.	.	PUNCT
ajbmeb-2644	44	1	if	if	SCONJ
ajbmeb-2644	44	2	log	log	VERB
ajbmeb-2644	44	3	3	3	NUM
ajbmeb-2644	44	4	x	x	SYM
ajbmeb-2644	44	5	log	log	VERB
ajbmeb-2644	44	6	3	3	NUM
ajbmeb-2644	44	7	7	7	NUM
ajbmeb-2644	44	8	2log	2log	PROPN
ajbmeb-2644	44	9	3	3	NUM
ajbmeb-2644	44	10	5	5	NUM
ajbmeb-2644	44	11	3log	3log	NUM
ajbmeb-2644	44	12	3	3	NUM
ajbmeb-2644	44	13	2	2	NUM
ajbmeb-2644	44	14	bo`lsa	bo`lsa	NOUN
ajbmeb-2644	44	15	,	,	PUNCT
ajbmeb-2644	44	16	x	x	PRON
ajbmeb-2644	44	17	find	find	VERB
ajbmeb-2644	44	18	.	.	PUNCT
ajbmeb-2644	45	1	2log	2log	NUM
ajbmeb-2644	45	2	3	3	NUM
ajbmeb-2644	45	3	2	2	NUM
ajbmeb-2644	45	4	3	3	NUM
ajbmeb-2644	45	5	log	log	NOUN
ajbmeb-2644	45	6	3	3	NUM
ajbmeb-2644	45	7	72	72	NUM
ajbmeb-2644	45	8	53	53	NUM
ajbmeb-2644	45	9	2	2	NUM
ajbmeb-2644	45	10	log	log	NOUN
ajbmeb-2644	45	11	3	3	NUM
ajbmeb-2644	45	12	1758	1758	NUM
ajbmeb-2644	45	13	,	,	PUNCT
ajbmeb-2644	45	14	solution	solution	NOUN
ajbmeb-2644	45	15	:	:	PUNCT
ajbmeb-2644	45	16	log	log	NOUN
ajbmeb-2644	45	17	3	3	NUM
ajbmeb-2644	45	18	x	x	SYM
ajbmeb-2644	45	19	log	log	VERB
ajbmeb-2644	45	20	3	3	NUM
ajbmeb-2644	45	21	7	7	NUM
ajbmeb-2644	45	22	log	log	NOUN
ajbmeb-2644	45	23	3	3	NUM
ajbmeb-2644	45	24	5	5	NUM
ajbmeb-2644	45	25	from	from	ADP
ajbmeb-2644	45	26	this	this	PRON
ajbmeb-2644	45	27	x	x	PUNCT
ajbmeb-2644	45	28	21,875	21,875	NUM
ajbmeb-2644	45	29	decimal	decimal	ADJ
ajbmeb-2644	45	30	and	and	CCONJ
ajbmeb-2644	45	31	natural	natural	ADJ
ajbmeb-2644	45	32	logarithms	logarithm	NOUN
ajbmeb-2644	45	33	.	.	PUNCT
ajbmeb-2644	46	1	definition	definition	NOUN
ajbmeb-2644	46	2	1	1	NUM
ajbmeb-2644	46	3	.	.	PUNCT
ajbmeb-2644	47	1	the	the	DET
ajbmeb-2644	47	2	basis	basis	NOUN
ajbmeb-2644	47	3	a=10	a=10	ADV
ajbmeb-2644	47	4	the	the	DET
ajbmeb-2644	47	5	logarithms	logarithm	NOUN
ajbmeb-2644	47	6	that	that	PRON
ajbmeb-2644	47	7	are	be	AUX
ajbmeb-2644	47	8	decimal	decimal	ADJ
ajbmeb-2644	47	9	logarithms	logarithm	NOUN
ajbmeb-2644	47	10	are	be	AUX
ajbmeb-2644	47	11	called	call	VERB
ajbmeb-2644	47	12	and	and	CCONJ
ajbmeb-2644	47	13	lgx	lgx	NOUN
ajbmeb-2644	47	14	is	be	AUX
ajbmeb-2644	47	15	expressed	express	VERB
ajbmeb-2644	47	16	through	through	ADP
ajbmeb-2644	47	17	,	,	PUNCT
ajbmeb-2644	47	18	i.e.	i.e.	X
ajbmeb-2644	47	19	log10x	log10x	NOUN
ajbmeb-2644	47	20	=	=	SYM
ajbmeb-2644	47	21	lgx	lgx	NOUN
ajbmeb-2644	47	22	7example.lg100	7example.lg100	NOUN
ajbmeb-2644	47	23	=	=	NOUN
ajbmeb-2644	47	24	lg102=2	lg102=2	ADJ
ajbmeb-2644	47	25	8	8	NUM
ajbmeb-2644	47	26	:	:	PUNCT
ajbmeb-2644	47	27	lg0,01	lg0,01	VERB
ajbmeb-2644	47	28	=	=	SYM
ajbmeb-2644	47	29	lg10	lg10	PROPN
ajbmeb-2644	47	30	-	-	PUNCT
ajbmeb-2644	47	31	2=-2	2=-2	NUM
ajbmeb-2644	47	32	2description	2description	NUM
ajbmeb-2644	47	33	.	.	PUNCT
ajbmeb-2644	48	1	a	a	DET
ajbmeb-2644	48	2	natural	natural	ADJ
ajbmeb-2644	48	3	logarithm	logarithm	NOUN
ajbmeb-2644	48	4	is	be	AUX
ajbmeb-2644	48	5	said	say	VERB
ajbmeb-2644	48	6	to	to	PART
ajbmeb-2644	48	7	be	be	AUX
ajbmeb-2644	48	8	a	a	DET
ajbmeb-2644	48	9	logarithm	logarithm	NOUN
ajbmeb-2644	48	10	whose	whose	DET
ajbmeb-2644	48	11	basis	basis	NOUN
ajbmeb-2644	48	12	is	be	AUX
ajbmeb-2644	48	13	a	a	DET
ajbmeb-2644	48	14	number	number	NOUN
ajbmeb-2644	48	15	e	e	NOUN
ajbmeb-2644	48	16	,	,	PUNCT
ajbmeb-2644	48	17	and	and	CCONJ
ajbmeb-2644	48	18	lnx	lnx	PROPN
ajbmeb-2644	48	19	is	be	AUX
ajbmeb-2644	48	20	defined	define	VERB
ajbmeb-2644	48	21	by	by	ADP
ajbmeb-2644	48	22	,	,	PUNCT
ajbmeb-2644	48	23	i.e.	i.e.	X
ajbmeb-2644	48	24	logex	logex	X
ajbmeb-2644	48	25	=	=	SYM
ajbmeb-2644	48	26	lnx	lnx	PROPN
ajbmeb-2644	48	27	,	,	PUNCT
ajbmeb-2644	48	28	e	e	PROPN
ajbmeb-2644	48	29	the	the	DET
ajbmeb-2644	48	30	number	number	NOUN
ajbmeb-2644	48	31	is	be	AUX
ajbmeb-2644	48	32	an	an	DET
ajbmeb-2644	48	33	irrational	irrational	ADJ
ajbmeb-2644	48	34	number	number	NOUN
ajbmeb-2644	48	35	,	,	PUNCT
ajbmeb-2644	48	36	e=2,7182818284	e=2,7182818284	NOUN
ajbmeb-2644	48	37	…	…	PUNCT
ajbmeb-2644	48	38	a	a	DET
ajbmeb-2644	48	39	in	in	ADP
ajbmeb-2644	48	40	practice	practice	NOUN
ajbmeb-2644	48	41	e≈2,7	e≈2,7	NOUN
ajbmeb-2644	48	42	can	can	AUX
ajbmeb-2644	48	43	be	be	AUX
ajbmeb-2644	48	44	taken	take	VERB
ajbmeb-2644	48	45	as	as	ADP
ajbmeb-2644	48	46	.	.	PUNCT
ajbmeb-2644	49	1	between	between	ADP
ajbmeb-2644	49	2	decimal	decimal	ADJ
ajbmeb-2644	49	3	and	and	CCONJ
ajbmeb-2644	49	4	natural	natural	ADJ
ajbmeb-2644	49	5	logarithms	logarithm	NOUN
ajbmeb-2644	49	6	lg	lg	NOUN
ajbmeb-2644	49	7	x	x	X
ajbmeb-2644	49	8	ln	ln	NOUN
ajbmeb-2644	49	9	x	x	X
ajbmeb-2644	49	10	0,434294ln	0,434294ln	NOUN
ajbmeb-2644	49	11	x	x	PUNCT
ajbmeb-2644	49	12	and	and	CCONJ
ajbmeb-2644	49	13	1	1	NUM
ajbmeb-2644	49	14	ln	ln	NOUN
ajbmeb-2644	49	15	x	x	X
ajbmeb-2644	49	16	lg	lg	NOUN
ajbmeb-2644	49	17	x	x	X
ajbmeb-2644	49	18	2,302551lg	2,302551lg	NUM
ajbmeb-2644	49	19	x	x	PUNCT
ajbmeb-2644	49	20	there	there	PRON
ajbmeb-2644	49	21	is	be	VERB
ajbmeb-2644	49	22	a	a	DET
ajbmeb-2644	49	23	link	link	NOUN
ajbmeb-2644	49	24	.	.	PUNCT
ajbmeb-2644	50	1	a	a	DET
ajbmeb-2644	50	2	in	in	ADP
ajbmeb-2644	50	3	practice	practice	NOUN
ajbmeb-2644	50	4	lg	lg	NOUN
ajbmeb-2644	50	5	x	x	X
ajbmeb-2644	50	6	0,4ln	0,4ln	PUNCT
ajbmeb-2644	50	7	x	x	X
ajbmeb-2644	50	8	and	and	CCONJ
ajbmeb-2644	50	9	lg	lg	PROPN
ajbmeb-2644	50	10	e	e	PROPN
ajbmeb-2644	50	11	ln	ln	NOUN
ajbmeb-2644	50	12	x	x	PROPN
ajbmeb-2644	50	13	2,3lg	2,3lg	NUM
ajbmeb-2644	50	14	x	x	NOUN
ajbmeb-2644	50	15	equalities	equality	NOUN
ajbmeb-2644	50	16	can	can	AUX
ajbmeb-2644	50	17	be	be	AUX
ajbmeb-2644	50	18	used	use	VERB
ajbmeb-2644	50	19	.	.	PUNCT
ajbmeb-2644	51	1	9example	9example	X
ajbmeb-2644	51	2	.	.	PUNCT
ajbmeb-2644	52	1	ln100	ln100	PROPN
ajbmeb-2644	52	2	,	,	PUNCT
ajbmeb-2644	52	3	lge2	lge2	NOUN
ajbmeb-2644	52	4	calculate	calculate	NOUN
ajbmeb-2644	52	5	.	.	PUNCT
ajbmeb-2644	53	1	ln100	ln100	PROPN
ajbmeb-2644	53	2	2,3	2,3	NUM
ajbmeb-2644	53	3	lg100	lg100	PROPN
ajbmeb-2644	53	4	2,3	2,3	NUM
ajbmeb-2644	53	5	2	2	NUM
ajbmeb-2644	53	6	4,6	4,6	NUM
ajbmeb-2644	53	7	.	.	PUNCT
ajbmeb-2644	54	1	solution	solution	NOUN
ajbmeb-2644	54	2	:	:	PUNCT
ajbmeb-2644	54	3	2	2	NUM
ajbmeb-2644	54	4	lg	lg	NOUN
ajbmeb-2644	54	5	e	e	NOUN
ajbmeb-2644	54	6	2lg	2lg	NOUN
ajbmeb-2644	54	7	e	e	NOUN
ajbmeb-2644	54	8	2	2	NUM
ajbmeb-2644	54	9	0,4ln	0,4ln	NUM
ajbmeb-2644	54	10	e	e	NOUN
ajbmeb-2644	54	11	0,8	0,8	NUM
ajbmeb-2644	54	12	.	.	PUNCT
ajbmeb-2644	55	1	american	american	PROPN
ajbmeb-2644	55	2	journal	journal	PROPN
ajbmeb-2644	55	3	of	of	ADP
ajbmeb-2644	55	4	business	business	NOUN
ajbmeb-2644	55	5	management	management	NOUN
ajbmeb-2644	55	6	,	,	PUNCT
ajbmeb-2644	55	7	economics	economic	NOUN
ajbmeb-2644	55	8	and	and	CCONJ
ajbmeb-2644	55	9	banking	banking	NOUN
ajbmeb-2644	55	10	volume	volume	NOUN
ajbmeb-2644	55	11	32	32	NUM
ajbmeb-2644	55	12	january	january	PROPN
ajbmeb-2644	55	13	2025	2025	NUM
ajbmeb-2644	55	14	p	p	NOUN
ajbmeb-2644	55	15	a	a	DET
ajbmeb-2644	55	16	g	g	NOUN
ajbmeb-2644	55	17	e	e	NOUN
ajbmeb-2644	56	1	|	|	ADV
ajbmeb-2644	56	2	34	34	NUM
ajbmeb-2644	56	3	www.americanjournal.org	www.americanjournal.org	PROPN
ajbmeb-2644	56	4	references	reference	NOUN
ajbmeb-2644	56	5	1	1	NUM
ajbmeb-2644	56	6	.	.	PUNCT
ajbmeb-2644	56	7	fundamentals	fundamental	NOUN
ajbmeb-2644	56	8	of	of	ADP
ajbmeb-2644	56	9	algebra	algebra	NOUN
ajbmeb-2644	56	10	and	and	CCONJ
ajbmeb-2644	56	11	analysis	analysis	NOUN
ajbmeb-2644	56	12	.	.	PUNCT
ajbmeb-2644	57	1	manual	manual	NOUN
ajbmeb-2644	57	2	for	for	ADP
ajbmeb-2644	57	3	academic	academic	ADJ
ajbmeb-2644	57	4	lyceums	lyceum	NOUN
ajbmeb-2644	57	5	(	(	PUNCT
ajbmeb-2644	57	6	r.x.vafoev	r.x.vafoev	PROPN
ajbmeb-2644	57	7	,	,	PUNCT
ajbmeb-2644	57	8	j.x.khusanov	j.x.khusanov	VERB
ajbmeb-2644	57	9	et	et	PROPN
ajbmeb-2644	57	10	al	al	PROPN
ajbmeb-2644	57	11	.	.	PROPN
ajbmeb-2644	58	1	t.	t.	PROPN
ajbmeb-2644	58	2	:	:	PUNCT
ajbmeb-2644	58	3	teacher	teacher	NOUN
ajbmeb-2644	58	4	,	,	PUNCT
ajbmeb-2644	58	5	2003	2003	NUM
ajbmeb-2644	58	6	-	-	SYM
ajbmeb-2644	58	7	368	368	NUM
ajbmeb-2644	58	8	p.	p.	NOUN
ajbmeb-2644	58	9	2.fundamentals	2.fundamentals	NUM
ajbmeb-2644	58	10	of	of	ADP
ajbmeb-2644	58	11	algebra	algebra	NOUN
ajbmeb-2644	58	12	and	and	CCONJ
ajbmeb-2644	58	13	mathematical	mathematical	ADJ
ajbmeb-2644	58	14	analysis	analysis	NOUN
ajbmeb-2644	58	15	.	.	PUNCT
ajbmeb-2644	59	1	i	i	PRON
ajbmeb-2644	59	2	k.	k.	PROPN
ajbmeb-2644	60	1	guide	guide	VERB
ajbmeb-2644	60	2	to	to	ADP
ajbmeb-2644	60	3	academic	academic	ADJ
ajbmeb-2644	60	4	lyceums	lyceum	NOUN
ajbmeb-2644	60	5	(	(	PUNCT
ajbmeb-2644	60	6	a.abdukhamidov	a.abdukhamidov	X
ajbmeb-2644	60	7	,	,	PUNCT
ajbmeb-2644	60	8	a.nasimov	a.nasimov	ADJ
ajbmeb-2644	60	9	et	et	PROPN
ajbmeb-2644	60	10	al	al	PROPN
ajbmeb-2644	60	11	.	.	PUNCT
ajbmeb-2644	61	1	t.	t.	PROPN
ajbmeb-2644	61	2	:	:	PUNCT
ajbmeb-2644	61	3	teacher	teacher	NOUN
ajbmeb-2644	61	4	,	,	PUNCT
ajbmeb-2644	61	5	2007	2007	NUM
ajbmeb-2644	61	6	.	.	PUNCT
ajbmeb-2644	62	1	462	462	NUM
ajbmeb-2644	62	2	b.	b.	PROPN
ajbmeb-2644	62	3	3.math	3.math	NUM
ajbmeb-2644	62	4	.	.	PUNCT
ajbmeb-2644	63	1	i	i	PRON
ajbmeb-2644	63	2	,	,	PUNCT
ajbmeb-2644	63	3	part	part	PROPN
ajbmeb-2644	63	4	ii	ii	PROPN
ajbmeb-2644	63	5	.	.	PUNCT
ajbmeb-2644	64	1	a	a	DET
ajbmeb-2644	64	2	manual	manual	NOUN
ajbmeb-2644	64	3	for	for	ADP
ajbmeb-2644	64	4	vocational	vocational	ADJ
ajbmeb-2644	64	5	colleges	college	NOUN
ajbmeb-2644	64	6	(	(	PUNCT
ajbmeb-2644	64	7	a.melikulov	a.melikulov	PROPN
ajbmeb-2644	64	8	et	et	PROPN
ajbmeb-2644	64	9	al	al	PROPN
ajbmeb-2644	64	10	.	.	PUNCT
ajbmeb-2644	65	1	t.	t.	PROPN
ajbmeb-2644	65	2	:	:	PUNCT
ajbmeb-2644	65	3	2003	2003	NUM
ajbmeb-2644	65	4	.	.	PUNCT