Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
40001	Simplify/Condense	-x log base 5 of 0.746	$- x \log_{5} (0.746)$
40002	Simplify/Condense	x log base b of r-x log base b of s-x log base b of t	$x \log_{b} (r) - x \log_{b} (s) - x \log_{b} (t)$
40003	Find the Domain	f(x) = natural log of 8-x	$f (x) = \ln (8 - x)$
40004	Simplify/Condense	log of x-2 log of y+5 log of z	$\log (x) - 2 \log (y) + 5 \log (z)$
40005	Simplify/Condense	log of x-3 log of y+4 log of z	$\log (x) - 3 \log (y) + 4 \log (z)$
40006	Simplify/Condense	log of x-5 log of x+1	$\log (x) - 5 \log (x + 1)$
40007	Simplify/Condense	log of x-5 log of y	$\log (x) - 5 \log (y)$
40008	Simplify/Condense	log of x- log of 15z	$\log (x) - \log (15 z)$
40009	Simplify/Condense	log of x- log of 5	$\log (x) - \log (5)$
40010	Simplify/Condense	log of x- log of x-1	$\log (x) - \log (x - 1)$
40011	Simplify/Condense	log of x- log of x-2	$\log (x) - \log (x - 2)$
40012	Simplify/Condense	log of x-7 log of y+9 log of z	$\log (x - 7) \log (y) + 9 \log (z)$
40013	Simplify/Condense	log of x-7 log of y+8 log of z	$\log (x - 7) \log (y + 8) \log (z)$
40014	Simplify/Condense	log of x-8	$\log (x - 8)$
40015	Simplify/Condense	log of x-9+ log of x+4- log of x-3	$\log (x - 9) + \log (x + 4) - \log (x - 3)$
40016	Simplify/Condense	log of x-1+ log of x+1	$\log (x - 1) + \log (x + 1)$
40017	Simplify/Condense	log of x-2+ log of x+2-0.5 log of x^2+4	$\log (x - 2) + \log (x + 2) - 0.5 \log (x^{2} + 4)$
40018	Simplify/Condense	natural log of x^2-4y^2-2 natural log of x-2y- natural log of 7	$\ln (x^{2} - 4 y^{2}) - 2 \ln (x - 2 y) - \ln (7)$
40019	Simplify/Condense	log of x^2-9-5 log of x+3	$\log (x^{2} - 9) - 5 \log (x + 3)$
40020	Simplify/Condense	log of a+3 log of b- log of c	$\log (a) + 3 \log (b) - \log (c)$
40021	Simplify/Condense	log of a+5 log of q	$\log (a) + 5 \log (q)$
40022	Simplify/Condense	log of a+6 log of b	$\log (a) + 6 \log (b)$
40023	Simplify/Condense	log of a+ log of b^2- log of c^3	$\log (a) + \log (b^{2}) - \log (c^{3})$
40024	Simplify/Condense	log of a+ log of b- log of c	$\log (a) + \log (b) - \log (c)$
40025	Simplify/Condense	log of a-6(21 log of b- log of c)	$\log (a) - 6 (21 \log (b) - \log (c))$
40026	Simplify/Condense	log of a- log of b	$\log (a) - \log (b)$
40027	Simplify/Condense	log of bx^7	$\log (b) x^{7}$
40028	Simplify	sec(theta)cos(theta)	$\sec (θ) \cos (θ)$
40029	Simplify/Condense	log of bxy	$\log (b) x y$
40030	Simplify/Condense	log of c+ log of a+ log of b+ log of i+ log of n	$\log (c) + \log (a) + \log (b) + \log (i) + \log (n)$
40031	Simplify/Condense	log of e- log of e^6- log of 6e	$\log (e) - \log (e^{6}) - \log (6 e)$
40032	Simplify/Condense	log of log of 10^10000	$\log (\log (10^{10000}))$
40033	Simplify/Condense	log of log of 100^(5x)	$\log (\log (100^{5 x}))$
40034	Simplify/Condense	log of log of 10000^(25x)	$\log (\log (10000^{25 x}))$
40035	Simplify/Condense	log of log of 100000^(200x)	$\log (\log (100000^{200 x}))$
40036	Simplify/Condense	log of log of 100000^(2x)	$\log (\log (100000^{2 x}))$
40037	Simplify/Condense	log of M+1/2* log of N	$\log (M) + \frac{1}{2} \cdot \log (N)$
40038	Simplify/Condense	( log of 9 fifth root of 3)/81	$\frac{\log (9) \sqrt[5]{3}}{81}$
40039	Simplify/Condense	log of 9+ log of 3	$\log (9) + \log (3)$
40040	Simplify/Condense	log of 9*(5 square root of 81)	$\log (9) \cdot (5 \sqrt{81})$
40041	Simplify/Condense	log of 9- log of 8	$\log (9) - \log (8)$
40042	Simplify/Condense	- log of 9.32+7	$- \log (9.32) + 7$
40043	Simplify/Condense	log of 97	$\log (97)$
40044	Simplify/Condense	log of 999- log of 1000	$\log (999) - \log (1000)$
40045	Simplify/Condense	log of a(sin(a))/(cos(a))cos(a/(sin(a)))	$\log (a) \cdot \frac{\sin (a)}{\cos (a)} \cdot \cos (\frac{a}{\sin (a)})$
40046	Simplify/Condense	log of ax^3y^2z	$\log (a) x^{3} y^{2} z$
40047	Simplify/Condense	log of 8*10^-7	$\log (8 \cdot 10^{- 7})$
40048	Simplify/Condense	log of 8 square root of 2	$\log (8 \sqrt{2})$
40049	Simplify/Condense	log of 80- log of 10	$\log (80) - \log (10)$
40050	Simplify/Condense	log of pq	$\log (p q)$
40051	Simplify/Condense	log of u+ log of v+ log of w	$\log (u) + \log (v) + \log (w)$
40052	Simplify/Condense	log of square root of 27	$\log (\sqrt{27})$
40053	Simplify/Condense	log of x+1/( log of x)	$\log (x) + \frac{1}{\log (x)}$
40054	Simplify/Condense	log of x+2 log of x+2 log of y	$\log (x) + 2 \log (x) + 2 \log (y)$
40055	Simplify/Condense	log of x+15 = log of x+ log of 15	$\log (x + 15) = \log (x) + \log (15)$
40056	Simplify/Condense	log of x+19+2 log of x-19- log of x^2-361	$\log (x + 19) + 2 \log (x - 19) - \log (x^{2} - 361)$
40057	Simplify/Condense	log of x+20+2 log of x-20- log of x^2-400	$\log (x + 20) + 2 \log (x - 20) - \log (x^{2} - 400)$
40058	Simplify/Condense	log of x+ log of x^2-64- log of 8- log of x+8	$\log (x) + \log (x^{2} - 64) - \log (8) - \log (x + 8)$
40059	Simplify/Condense	log of x+ log of x^2-64- log of 7- log of x-8	$\log (x) + \log (x^{2} - 64) - \log (7) - \log (x - 8)$
40060	Simplify/Condense	log of x+ log of x^2-81- log of 3- log of x-9	$\log (x) + \log (x^{2} - 81) - \log (3) - \log (x - 9)$
40061	Simplify/Condense	log of x+ log of x^2-9- log of 3- log of x+3	$\log (x) + \log (x^{2} - 9) - \log (3) - \log (x + 3)$
40062	Simplify/Condense	log of x+ log of x^2-4- log of x- log of x+2	$\log (x) + \log (x^{2} - 4) - \log (x) - \log (x + 2)$
40063	Simplify/Condense	log of x+ log of x^2-49- log of 2- log of x+7	$\log (x) + \log (x^{2} - 49) - \log (2) - \log (x + 7)$
40064	Simplify/Condense	log of x* log of x	$\log (x) \cdot \log (x)$
40065	Simplify/Condense	log of x-1/2* log of y+3 log of z	$\log (x) - \frac{1}{2} \cdot \log (y) + 3 \log (z)$
40066	Simplify/Condense	log of x-2 log of y+2 log of z	$\log (x) - 2 \log (y) + 2 \log (z)$
40067	Simplify/Condense	log of x=-2.1	$\log (x) = - 2.1$
40068	Simplify/Condense	log of x+ log of x^2-9- log of 7- log of x-3	$\log (x) + \log (x^{2} - 9) - \log (7 - \log (x - 3))$
40069	Simplify/Condense	log of x+ log of x^2-9- log of 9- log of x+3	$\log (x) + \log (x^{2} - 9) - \log (9) - \log (x + 3)$
40070	Simplify/Condense	log of x+ log of x^2y+3 log of y	$\log (x) + \log (x^{2} y) + 3 \log (y)$
40071	Simplify/Condense	log of x+ log of 15	$\log (x) + \log (15)$
40072	Simplify/Condense	log of x+ log of 7+ log of x^2-1- log of x+1	$\log (x) + \log (7) + \log (x^{2} - 1) - \log (x + 1)$
40073	Simplify/Condense	log of x+ log of x+4 log of 45	$\log (x) + \log (x + 4) \log (45)$
40074	Simplify/Condense	log of x+ log of x-3 log of 40	$\log (x) + \log (x - 3) \log (40)$
40075	Simplify/Condense	log of x+ log of x-9	$\log (x) + \log (x - 9)$
40076	Evaluate	arctan(2.607)	$\arctan (2.607)$
40077	Simplify/Condense	log of x+ log of x^2-36- log of 5- log of x+6	$\log (x) + \log (x^{2} - 36) - \log (5) - \log (x + 6)$
40078	Simplify/Condense	log of x+ log of x^2-4- log of 15- log of x+2	$\log (x) + \log (x^{2} - 4) - \log (15) - \log (x + 2)$
40079	Simplify/Condense	log of x+ log of x^2-4- log of 5- log of x+2	$\log (x) + \log (x^{2} - 4) - \log (5) - \log (x + 2)$
40080	Simplify/Condense	log of x+4 log of (x)^2-3 log of (x)^3	$\log (x) + 4 \log ({(x)}^{2}) - 3 \log ({(x)}^{3})$
40081	Simplify/Condense	log of x+ log of x^2+1- log of 7- log of x+1	$\log (x) + \log (x^{2} + 1) - \log (7) - \log (x + 1)$
40082	Simplify/Condense	log of x+ log of x^2-1-2 log of x- log of x+1	$\log (x) + \log (x^{2} - 1) - 2 \log (x) - \log (x + 1)$
40083	Simplify/Condense	log of x+ log of x^2-100- log of 8- log of x-10	$\log (x) + \log (x^{2} - 100) - \log (8) - \log (x - 10)$
40084	Simplify/Condense	log of x+ log of x^2-16- log of 11- log of x+4	$\log (x) + \log (x^{2} - 16) - \log (11) - \log (x + 4)$
40085	Simplify/Condense	log of x+ log of x^2-196- log of 7- log of x-14	$\log (x) + \log (x^{2} - 196) - \log (7) - \log (x - 14)$
40086	Simplify/Condense	5^( log base 5 of 32)	$5^{\log_{5} (32)}$
40087	Simplify/Condense	7/2* log base n of 5y+4/7* log base n of 25y^2	$\frac{7}{2} \cdot \log_{n} (5 y + \frac{4}{7} \cdot \log_{n} (25 y^{2}))$
40088	Simplify/Condense	7^( log base 7 of 3)	$7^{\log_{7} (3)}$
40089	Simplify/Condense	7^( log of 7(2))	$7^{\log (7) (2)}$
40090	Simplify/Condense	e^(2 natural log of 6- natural log of 2)	$e^{2 \ln (6) - \ln (2)}$
40091	Simplify/Condense	e^(3 natural log of x^2)	$e^{3 \ln (x^{2})}$
40092	Simplify/Condense	e^(4-7 natural log of x+ natural log of y)	$e^{4 - 7 \ln (x) + \ln (y)}$
40093	Simplify/Condense	e^(4 natural log of x-2)	$e^{4 \ln (x - 2)}$
40094	Simplify/Condense	e^(7-3 natural log of x+ natural log of y)	$e^{7 - 3 \ln (x) + \ln (y)}$
40095	Simplify/Condense	e^( natural log of 1/x)	$e^{\ln (\frac{1}{x})}$
40096	Simplify/Condense	e^( natural log of 41)	$e^{\ln (41)}$
40097	Simplify/Condense	e^( natural log of x-2)	$e^{\ln (x - 2)}$
40098	Simplify/Condense	( natural log of 0.5)/600	$\frac{\ln (0.5)}{600}$
40099	Simplify/Condense	natural log of ((x^2-x-2)/((x+4)^5))^(1/3)	$\ln ({(\frac{x^{2} - x - 2}{{(x + 4)}^{5}})}^{\frac{1}{3}})$
40100	Simplify/Condense	( natural log of 1/7)/( natural log of 7)	$\frac{\ln (\frac{1}{7})}{\ln (7)}$