Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
22001	Simplify/Condense	1/2* natural log of x+1	$\frac{1}{2} \cdot \ln (x + 1)$
22002	Simplify/Condense	1/2*( natural log of x+4 natural log of y-5 natural log of z)	$\frac{1}{2} \cdot (\ln (x + 4) \ln (y - 5) \ln (z))$
22003	Simplify/Condense	1/2* natural log of x-1-3 natural log of x+4 natural log of 3x	$\frac{1}{2} \cdot \ln (x - 1) - 3 \ln (x) + 4 \ln (3 x)$
22004	Simplify/Condense	1/2* natural log of x-3+ natural log of x+2-6 natural log of x	$\frac{1}{2} \cdot \ln (x - 3) + \ln (x + 2) - 6 \ln (x)$
22005	Simplify/Condense	1/2* natural log of z- natural log of 1+x-2 natural log of y	$\frac{1}{2} \cdot \ln (z) - \ln (1 + x) - 2 \ln (y)$
22006	Simplify/Condense	1/2* log of 100	$\frac{1}{2} \cdot \log (100)$
22007	Simplify/Condense	1/2* log of 16-1/3* log of 8+1	$\frac{1}{2} \cdot \log (16) - \frac{1}{3} \cdot \log (8) + 1$
22008	Simplify/Condense	1/2*( log of 6x)+ log of 6y	$\frac{1}{2} \cdot (\log (6) x) + \log (6) y$
22009	Simplify/Condense	1/2* log of a+3 log of b	$\frac{1}{2} \cdot \log (a) + 3 \log (b)$
22010	Simplify/Condense	0.05-10 natural log of 0.09	$0.05 - 10 \ln (0.09)$
22011	Simplify/Condense	0.25(3 natural log of x+2- natural log of x- natural log of x^2-49)	$0.25 (3 \ln (x + 2 - \ln (x) - \ln (x^{2} - 49)))$
22012	Simplify/Condense	0.37* natural log of 119+0.05	$0.37 \cdot \ln (119 + 0.05)$
22013	Simplify/Condense	0.37* natural log of 74000+0.05	$0.37 \cdot \ln (74000) + 0.05$
22014	Simplify/Condense	0.5 log base x of y+5 log base x of z-3 log base x of y	$0.5 \log_{x} (y) + 5 \log_{x} (z) - 3 \log_{x} (y)$
22015	Simplify/Condense	0.5 natural log of 2x-1-2 natural log of x+1	$0.5 \ln (2 x - 1) - 2 \ln (x + 1)$
22016	Simplify/Condense	0.5 log of x	$0.5 \log (x)$
22017	Simplify/Condense	(( natural log of 15- natural log of 3)/( natural log of 75- natural log of 3))+ natural log of 9-1/2- natural log of 10* log of 9	$(\frac{\ln (15) - \ln (3)}{\ln (75) - \ln (3)}) + \ln (9) - \frac{1}{2} - \ln (10) \cdot \log (9)$
22018	Simplify/Condense	4 log base 3 of x+2 log base 3 of 4x- log base 3 of square root of x	$4 \log_{3} (x) + 2 \log_{3} (4 x) - \log_{3} (\sqrt{x})$
22019	Simplify/Condense	(4 log base 3 of x+6+7 log base 3 of x+4)-1/2* log base 3 of x	$(4 \log_{3} (x + 6) + 7 \log_{3} (x + 4)) - \frac{1}{2} \cdot \log_{3} (x)$
22020	Simplify/Condense	natural log of 3(( square root of x*y)/(pq^4))	$\ln (3) (\frac{\sqrt{x \cdot y}}{p q^{4}})$
22021	Simplify/Condense	log of z+3-2 log of z+5+5( log of z- log of x+3)	$\log (z + 3) - 2 \log (z + 5) + 5 (\log (z) - \log (x + 3))$
22022	Simplify/Condense	((4x+1)(7^x natural log of 7)-7^x*4)/((4x+1)^2)	$\frac{(4 x + 1) (7^{x} \ln (7)) - 7^{x} \cdot 4}{{(4 x + 1)}^{2}}$
22023	Simplify/Condense	(3^( natural log of x^2))^(1/( natural log of 3))	${(3^{\ln (x^{2})})}^{\frac{1}{\ln (3)}}$
22024	Simplify/Condense	(6037691714794393/23- fifth root of 89)/( log of 29583)(arctan(2598))/pi(2365522/33333333333333333* square root of 4)/100-4	$\frac{\frac{6037691714794393}{23} - \sqrt[5]{89}}{\log (29583)} \cdot \frac{\arctan (2598)}{π} \cdot \frac{\frac{2365522}{33333333333333333} \cdot \sqrt{4}}{100} - 4$
22025	Simplify/Condense	(e^(2 natural log of 2-3 natural log of 2+1))^2	${(e^{2 \ln (2) - 3 \ln (2) + 1})}^{2}$
22026	Simplify/Condense	( log base 8 of 3-8)/7	$\frac{\log_{8} (3) - 8}{7}$
22027	Simplify/Condense	(1+ log base 9 of x)/2	$\frac{1 + \log_{9} (x)}{2}$
22028	Simplify/Condense	(2+ax)^10	${(2 + a x)}^{10}$
22029	Simplify/Condense	(4 natural log of 3)/( natural log of 2)+(5 natural log of 3)/( natural log of 2)	$\frac{4 \ln (3)}{\ln (2)} + \frac{5 \ln (3)}{\ln (2)}$
22030	Simplify/Condense	(4 log of 36-x^2-( log of 6+x+ log of 6-x))/((6+x)(6-x))	$\frac{4 \log (36 - x^{2}) - (\log (6 + x) + \log (6 - x))}{(6 + x) (6 - x)}$
22031	Simplify/Condense	( natural log of 3- natural log of 1)/3	$\frac{\ln (3) - \ln (1)}{3}$
22032	Simplify/Condense	( log of x(9x))/2	$\frac{\log (x) (9 x)}{2}$
22033	Simplify/Condense	log of x-1/3* log of z+1/2* log of y	$\log (x) - \frac{1}{3} \cdot \log (z) + \frac{1}{2} \cdot \log (y)$
22034	Simplify/Condense	log of x- log base 3 of 10	$\log (x) - \log_{3} (10)$
22035	Simplify/Condense	log of x+ log of x^2-16- log of 5- log of x-4	$\log (x) + \log (x^{2} - 16) - \log (5) - \log (x - 4)$
22036	Simplify/Condense	log of x+ log of x^2-36- log of 9- log of x+6	$\log (x) + \log (x^{2} - 36) - \log (9) - \log (x + 6)$
22037	Simplify/Condense	log of x+ log of x^2-49- log of 8- log of x+7	$\log (x) + \log (x^{2} - 49) - \log (8) - \log (x + 7)$
22038	Simplify/Condense	log of x+ log of x^2-81- log of 7- log of x+9	$\log (x) + \log (x^{2} - 81) - \log (7) - \log (x + 9)$
22039	Simplify/Condense	log of x+ log of y-2 log of z	$\log (x) + \log (y) - 2 \log (z)$
22040	Simplify/Condense	log of x log of x^2-169- log of 9- log of x-13	$\log (x) \log (x^{2} - 169) - \log (9) - \log (x - 13)$
22041	Simplify/Condense	log of x- log of x^2-81- log of 4- log of x-9	$\log (x) - \log (x^{2} - 81) - \log (4) - \log (x - 9)$
22042	Simplify/Condense	log of x- log of 7- log of 8	$\log (x) - \log (7) - \log (8)$
22043	Simplify/Condense	log of 5+ log of 6	$\log (5) + \log (6)$
22044	Simplify/Condense	log of 5- log of 3x^2	$\log (5) - \log (3 x^{2})$
22045	Simplify/Condense	log of 6- log of 15x+ log of 7x+ log of 10	$\log (6) - \log (15 x) + \log (7 x) + \log (10)$
22046	Simplify/Condense	log of 7(c^2 square root of (a^3)/(b^5))	$\log (7) (c^{2} \sqrt{\frac{a^{3}}{b^{5}}})$
22047	Simplify/Condense	log of 3.2+ log of 5.7	$\log (3.2) + \log (5.7)$
22048	Simplify/Condense	log of 30+ log of 2	$\log (30) + \log (2)$
22049	Simplify/Condense	log of 343	$\log (343)$
22050	Simplify/Condense	log of 36- log of 4	$\log (36) - \log (4)$
22051	Simplify/Condense	log of 3x-2( log of x- log of 2+y)	$\log (3 x - 2) (\log (x) - \log (2 + y))$
22052	Simplify/Condense	log of 4(x-4)	$\log (4) (x - 4)$
22053	Simplify/Condense	log of x-3-2 log of x+9 log of x+1	$\log (x - 3) - 2 \log (x) + 9 \log (x + 1)$
22054	Simplify/Condense	log of x-4- log of x^2-16	$\log (x - 4) - \log (x^{2} - 16)$
22055	Simplify/Condense	log of xy-3 log of w	$\log (x y) - 3 \log (w)$
22056	Simplify/Condense	p log base b of A-q log base b of B+r log base b of C	$p \log_{b} (A) - q \log_{b} (B) + r \log_{b} (C)$
22057	Simplify/Condense	x log of 15	$x \log (15)$
22058	Simplify/Condense	x log base 2 of m+1/y* log base 2 of n- log base 2 of p	$x \log_{2} (m) + \frac{1}{y} \cdot \log_{2} (n) - \log_{2} (p)$
22059	Simplify/Condense	x- natural log of 4	$x - \ln (4)$
22060	Simplify/Condense	x natural log of x	$x \ln (x)$
22061	Simplify/Condense	\|2 natural log of x+6- natural log of x- natural log of x^2-36\|	$\| 2 \ln (x + 6) - \ln (x) - \ln (x^{2} - 36) \|$
22062	Simplify/Condense	(( natural log of 30- natural log of 3)/( natural log of 100- natural log of 1))+ natural log of 9-1/2- natural log of 10* log of 9	$(\frac{\ln (30) - \ln (3)}{\ln (100) - \ln (1)}) + \ln (9) - \frac{1}{2} - \ln (10) \cdot \log (9)$
22063	Simplify/Condense	((( log of 12)/( log of 3))/2)+1	$(\frac{\frac{\log (12)}{\log (3)}}{2}) + 1$
22064	Simplify/Condense	(1/2) log base 6 of 9+ log base 6 of 5	$(\frac{1}{2}) \log_{6} (9) + \log_{6} (5)$
22065	Simplify/Condense	(1/2) natural log of 49	$(\frac{1}{2}) \ln (49)$
22066	Simplify/Condense	(1/2) natural log of x- natural log of 8	$(\frac{1}{2}) \ln (x) - \ln (8)$
22067	Simplify/Condense	(1/2) log of 3(1/81)	$(\frac{1}{2}) \log (3) (\frac{1}{81})$
22068	Simplify/Condense	(1/2) log of x-3 log of y+2 log of 8- log of t	$(\frac{1}{2}) \log (x) - 3 \log (y) + 2 \log (8) - \log (t)$
22069	Simplify/Condense	(1/3) log base 2 of x+(2/3) log base 2 of x- log base 2 of y	$(\frac{1}{3}) \log_{2} (x) + (\frac{2}{3}) \log_{2} (x) - \log_{2} (y)$
22070	Simplify/Condense	(1/3) natural log of 2-1-1/3 natural log of 2	$(\frac{1}{3}) \ln (2 - 1) - \frac{1}{3} \ln (2)$
22071	Simplify/Condense	(1/3) natural log of 4-1-1/3 natural log of 2	$(\frac{1}{3}) \ln (4 - 1) - \frac{1}{3} \ln (2)$
22072	Simplify/Condense	(1/3) log of 64-1/2 log of 49	$(\frac{1}{3}) \log (64) - \frac{1}{2} \log (49)$
22073	Simplify/Condense	(-1/3) log of 8	$(- \frac{1}{3}) \log (8)$
22074	Simplify/Condense	1/3* natural log of 2x-3+1/3* natural log of 3x+2-(2/3* natural log of x^2-1)	$\frac{1}{3} \cdot \ln (2 x - 3) + \frac{1}{3} \cdot \ln (3 x + 2) - (\frac{2}{3} \cdot \ln (x^{2}) - 1)$
22075	Simplify/Condense	(1/4) log of x-4 log of y-3 log of z	$(\frac{1}{4}) \log (x) - 4 \log (y) - 3 \log (z)$
22076	Simplify/Condense	(1/4* log of 16)-(2 log of 5)+ log of 7	$(\frac{1}{4} \cdot \log (16)) - (2 \log (5)) + \log (7)$
22077	Simplify/Condense	(1/5)(3 log of x+1+2 log of x-1- log of 7)	$(\frac{1}{5}) (3 \log (x + 1) + 2 \log (x - 1) - \log (7))$
22078	Simplify/Condense	(4/3) log base 3 of x-2 log base 3 of y+(1/2) log base 3 of z	$(\frac{4}{3}) \log_{3} (x) - 2 \log_{3} (y) + (\frac{1}{2}) \log_{3} (z)$
22079	Simplify/Condense	-e^(-0.14)-e^(-0.13)+5( natural log of 4- natural log of 3)	$- e^{- 0.1 \cdot 4} - e^{- 0.1 \cdot 3} + 5 (\ln (4) - \ln (3))$
22080	Simplify/Condense	natural log of (4)^2-4 natural log of 4	$\ln ({(4)}^{2}) - 4 \ln (4)$
22081	Simplify/Condense	( log base 0.5 of x)+2	$(\log_{0.5} (x)) + 2$
22082	Simplify/Condense	log base 2 of x^2+2x+1+ log base 2 of x+1	$\log_{2} (x^{2} + 2 x + 1) + \log_{2} (x + 1)$
22083	Simplify/Condense	( log base 6 of 5)( log base 5 of 7)	$(\log_{6} (5)) (\log_{5} (7))$
22084	Simplify/Condense	( log base 7 of 2.2)*-1	$(\log_{7} (2.2)) \cdot - 1$
22085	Simplify/Condense	( log base 7 of 5)*( log base 5 of 8)	$(\log_{7} (5)) \cdot (\log_{5} (8))$
22086	Simplify/Condense	( log base 8 of 7)( log base 7 of 9)	$(\log_{8} (7)) (\log_{7} (9))$
22087	Simplify/Condense	( log base 8 of 9)( log base 9 of 10)( log of 11)	$(\log_{8} (9)) (\log_{9} (10)) (\log (11))$
22088	Simplify/Condense	( log base 8 of x)-8	$(\log_{8} (x)) - 8$
22089	Simplify/Condense	( log base 9 of 10)( log of 11)( log base 11 of 12)	$(\log_{9} (10)) (\log (11)) (\log_{11} (12))$
22090	Simplify/Condense	( log base 9 of 96)-(5 log base 9 of 2)-4	$(\log_{9} (96)) - (5 \log_{9} (2)) - 4$
22091	Simplify/Condense	( log base 9 of 96)-(5 log base 9 of 2-4)	$(\log_{9} (96)) - (5 \log_{9} (2 - 4))$
22092	Simplify/Condense	( log base b of 93.1699)( log base b of 52.3219) log base b of 225	$(\log_{b} (9) \cdot 3.1699) (\log_{b} (5) \cdot 2.3219) \log_{b} (225)$
22093	Simplify/Condense	( log base b of a)( log base d of b( log base c of d))	$(\log_{b} (a)) (\log_{d} (b) (\log_{c} (d)))$
22094	Simplify/Condense	( log base z of x)*( log base z of y)	$(\log_{z} (x)) \cdot (\log_{z} (y))$
22095	Simplify/Condense	(n^4+n^3 log of n)( log of n+7)+(14 log of n+18)(n^4+16)	$(n^{4} + n^{3} \log (n)) (\log (n) + 7) + (14 \log (n) + 18) (n^{4} + 16)$
22096	Simplify/Condense	(2 natural log of e^2-1/2)( natural log of e^4)+ natural log of e	$(2 \ln (e^{2}) - \frac{1}{2}) (\ln (e^{4})) + \ln (e)$
22097	Simplify/Condense	(2 log of 4)-( log of 3)+2 log of 43.3012-4	$(2 \log (4)) - (\log (3)) + 2 \log (43.3012 - 4)$
22098	Simplify/Condense	(3 log of (x)^2)+1	$(3 \log ({(x)}^{2})) + 1$
22099	Simplify/Condense	(30 log of 6)-(5 log of 11)	$(30 \log (6)) - (5 \log (11))$
22100	Simplify/Condense	(cos(x))( log base 3 of x+1)(arcsin(x))	$(\cos (x)) \cdot (\log_{3} (x + 1)) \cdot (\arcsin (x))$