Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
23001	Simplify/Condense	2 log base 5 of 18- log base 5 of 3+1/2* log base 5 of 16	$2 \log_{5} (18 - \log_{5} (3)) + \frac{1}{2} \cdot \log_{5} (16)$
23002	Simplify/Condense	2 log base 5 of 5x- log base 5 of (x)^2	$2 \log_{5} (5 x) - \log_{5} ({(x)}^{2})$
23003	Simplify/Condense	-2 log base 5 of 7x=2	$- 2 \log_{5} (7 x) = 2$
23004	Simplify/Condense	2 log base 5 of u+9 log base 5 of v	$2 \log_{5} (u) + 9 \log_{5} (v)$
23005	Simplify/Condense	2 log base 5 of w+2( log base 5 of z-5 log base 5 of x)	$2 \log_{5} (w) + 2 (\log_{5} (z) - 5 \log_{5} (x))$
23006	Simplify/Condense	3 log base 4 of x^2-4 log base 4 of x+5 log base 4 of x	$3 \log_{4} (x^{2}) - 4 \log_{4} (x) + 5 \log_{4} (x)$
23007	Simplify/Condense	3 log base 4 of x^5-4 log base 4 of x^-2+4 log base 4 of x	$3 \log_{4} (x^{5}) - 4 \log_{4} (x^{- 2}) + 4 \log_{4} (x)$
23008	Simplify/Condense	3 log base 4 of 14-3 log base 4 of 42	$3 \log_{4} (14) - 3 \log_{4} (42)$
23009	Simplify/Condense	-3 log base 4 of 4x	$- 3 \log_{4} (4 x)$
23010	Simplify/Condense	3 log base 4 of 5x-6+4 log base 4 of 3x-3	$3 \log_{4} (5 x - 6) + 4 \log_{4} (3 x - 3)$
23011	Simplify/Condense	3 log base 4 of 6x=9	$3 \log_{4} (6 x) = 9$
23012	Simplify/Condense	3 log base 4 of A+2 log base 4 of B-3 log base 4 of C	$3 \log_{4} (A) + 2 \log_{4} (B) - 3 \log_{4} (C)$
23013	Simplify/Condense	3 log base 4 of a+2 log base 4 of b-5 log base 4 of c	$3 \log_{4} (a) + 2 \log_{4} (b) - 5 \log_{4} (c)$
23014	Simplify/Condense	3 log base 3 of 7-6 log base 6 of 2	$3 \log_{3} (7) - 6 \log_{6} (2)$
23015	Simplify/Condense	3 log base 3 of 8	$3 \log_{3} (8)$
23016	Simplify/Condense	3 log base 3 of A-2 log base 3 of B-5 log base 3 of C+1/2* log base 3 of D	$3 \log_{3} (A) - 2 \log_{3} (B) - 5 \log_{3} (C) + \frac{1}{2} \cdot \log_{3} (D)$
23017	Simplify/Condense	3 log base 3 of x- log base 3 of 1/y	$3 \log_{3} (x) - \log_{3} (\frac{1}{y})$
23018	Simplify/Condense	3 log base 4 of x+2 log base 4 of x	$3 \log_{4} (x) + 2 \log_{4} (x)$
23019	Simplify/Condense	3 log base 4 of x+4( log base 4 of w-3 log base 4 of z)	$3 \log_{4} (x) + 4 (\log_{4} (w) - 3 \log_{4} (z))$
23020	Simplify/Condense	3 log base 4 of x+9 log base 4 of y	$3 \log_{4} (x) + 9 \log_{4} (y)$
23021	Simplify/Condense	3 log base 4 of x-1	$3 \log_{4} (x - 1)$
23022	Simplify/Condense	3 log base 5 of 3+1/5* log base 5 of x-4-1/2* log base 5 of x	$3 \log_{5} (3) + \frac{1}{5} \cdot \log_{5} (x - 4) - \frac{1}{2} \cdot \log_{5} (x)$
23023	Simplify/Condense	3 log base 5 of 3x+1-2 log base 5 of 2x-1	$3 \log_{5} (3 x + 1) - 2 \log_{5} (2 x - 1)$
23024	Simplify/Condense	3 log base 5 of u+2 log base 5 of v	$3 \log_{5} (u) + 2 \log_{5} (v)$
23025	Simplify/Condense	3 log base 5 of u+4 log base 5 of v	$3 \log_{5} (u) + 4 \log_{5} (v)$
23026	Simplify/Condense	3 log base 2 of x-1/2* log base 2 of y	$3 \log_{2} (x) - \frac{1}{2} \cdot \log_{2} (y)$
23027	Simplify/Condense	3 log base 3 of x-4 log base 3 of y	$3 \log_{3} (x) - 4 \log_{3} (y)$
23028	Simplify/Condense	3 log base 3 of x-2 log base 3 of y	$3 \log_{3} (x - 2 \log_{3} (y))$
23029	Simplify/Condense	3 log base 3 of x-5+1/3* log base 3 of x+5	$3 \log_{3} (x - 5) + \frac{1}{3} \cdot \log_{3} (x + 5)$
23030	Simplify/Condense	3 log base a of 6x^4-1/7* log base a of 4x+13	$3 \log_{a} (6 x^{4}) - \frac{1}{7} \cdot \log_{a} (4 x + 13)$
23031	Simplify/Condense	3 log base a of 7x^4-1/8* log base a of 4x+17	$3 \log_{a} (7 x^{4}) - \frac{1}{8} \cdot \log_{a} (4 x + 17)$
23032	Simplify/Condense	3 log base b of x+7 log base b of z	$3 \log_{b} (x) + 7 \log_{b} (z)$
23033	Simplify/Condense	3 log base b of x+8 log base b of z	$3 \log_{b} (x) + 8 \log_{b} (z)$
23034	Simplify/Condense	-3 log base b of x-2 log base b of y+1/2* log base b of z	$- 3 \log_{b} (x) - 2 \log_{b} (y) + \frac{1}{2} \cdot \log_{b} (z)$
23035	Simplify/Condense	3 log base b of x+6 log base b of z	$3 \log_{b} (x + 6 \log_{b} (z))$
23036	Simplify/Condense	3 log base b of x+9 log base b of z	$3 \log_{b} (x + 9) \log_{b} (z)$
23037	Simplify/Condense	3 log base c of m-5/6* log base c of n+1/4* log base c of j-6 log base c of k	$3 \log_{c} (m) - \frac{5}{6} \cdot \log_{c} (n) + \frac{1}{4} \cdot \log_{c} (j) - 6 \log_{c} (k)$
23038	Simplify/Condense	3 log base c of x-5 log base c of y^4	$3 \log_{c} (x) - 5 \log_{c} (y^{4})$
23039	Simplify/Condense	3 log base x of 4+ log base x of 2	$3 \log_{x} (4) + \log_{x} (2)$
23040	Simplify/Condense	3+3 log of x+5 log of y	$3 + 3 \log (x) + 5 \log (y)$
23041	Simplify/Condense	30 log base 2 of u+6 log base 2 of v	$30 \log_{2} (u) + 6 \log_{2} (v)$
23042	Simplify/Condense	3 natural log of e^(4x)	$3 \ln (e^{4 x})$
23043	Simplify/Condense	3 natural log of square root of x+1/2* natural log of x	$3 \ln (\sqrt{x}) + \frac{1}{2} \cdot \ln (x)$
23044	Find the Domain	h(t)=(2t-6)/(t^2+6t+9)	$h (t) = \frac{2 t - 6}{t^{2} + 6 t + 9}$
23045	Simplify/Condense	3 natural log of 2	$3 \ln (2)$
23046	Simplify/Condense	3 natural log of 2+ natural log of 3	$3 \ln (2) + \ln (3)$
23047	Simplify/Condense	3 natural log of 2- natural log of 4	$3 \ln (2) - \ln (4)$
23048	Simplify/Condense	-3 natural log of 3x^2	$- 3 \ln (3 x^{2})$
23049	Simplify/Condense	-3 natural log of 5x^3+4 natural log of 3x^4	$- 3 \ln (5 x^{3}) + 4 \ln (3 x^{4})$
23050	Simplify/Condense	3 natural log of 7x	$3 \ln (7 x)$
23051	Simplify/Condense	3 natural log of a	$3 \ln (a)$
23052	Simplify/Condense	3 natural log of a-1/2*( natural log of b+ natural log of c^2)	$3 \ln (a) - \frac{1}{2} \cdot (\ln (b) + \ln (c^{2}))$
23053	Simplify/Condense	3 natural log of e+4 natural log of e^2-2 natural log of e	$3 \ln (e) + 4 \ln (e^{2}) - 2 \ln (e)$
23054	Simplify/Condense	3 natural log of x-1/2* natural log of 16	$3 \ln (x) - \frac{1}{2} \cdot \ln (16)$
23055	Simplify/Condense	3 natural log of x-1/2* natural log of y+1/3* natural log of z	$3 \ln (x) - \frac{1}{2} \cdot \ln (y) + \frac{1}{3} \cdot \ln (z)$
23056	Simplify/Condense	3 natural log of x-1/4* natural log of y	$3 \ln (x) - \frac{1}{4} \cdot \ln (y)$
23057	Simplify/Condense	3 natural log of x-1/6* natural log of y	$3 \ln (x) - \frac{1}{6} \cdot \ln (y)$
23058	Simplify/Condense	3 natural log of x-1/8* natural log of y	$3 \ln (x) - \frac{1}{8} \cdot \ln (y)$
23059	Simplify/Condense	3 natural log of x-1/9* natural log of y	$3 \ln (x) - \frac{1}{9} \cdot \ln (y)$
23060	Simplify/Condense	3 natural log of x-3/2* natural log of y+4 natural log of z	$3 \ln (x) - \frac{3}{2} \cdot \ln (y) + 4 \ln (z)$
23061	Simplify/Condense	3 log base 5 of x+3/2* log base 5 of y- log base 5 of 5z	$3 \log_{5} (x) + \frac{3}{2} \cdot \log_{5} (y) - \log_{5} (5 z)$
23062	Simplify/Condense	3 log base 5 of x+2 log base 5 of y-8 log base 5 of z	$3 \log_{5} (x) + 2 \log_{5} (y) - 8 \log_{5} (z)$
23063	Simplify/Condense	3 log base 5 of x+4 log base 5 of y- log base 5 of z-2 log base 5 of 4	$3 \log_{5} (x) + 4 \log_{5} (y) - \log_{5} (z) - 2 \log_{5} (4)$
23064	Simplify/Condense	3 log base 5 of x+7 log base 5 of y-2 log base 5 of z	$3 \log_{5} (x) + 7 \log_{5} (y) - 2 \log_{5} (z)$
23065	Simplify/Condense	3 log base 5 of x+9 log base 5 of y-12 log base 5 of z	$3 \log_{5} (x) + 9 \log_{5} (y) - 12 \log_{5} (z)$
23066	Simplify/Condense	3 log base 5 of x-2 log base 5 of y-4 log base 5 of z	$3 \log_{5} (x) - 2 \log_{5} (y) - 4 \log_{5} (z)$
23067	Simplify/Condense	3 log base 5 of x+6- log base 5 of x-10- log base 5 of x-4	$3 \log_{5} (x + 6) - \log_{5} (x - 10) - \log_{5} (x - 4)$
23068	Simplify/Condense	3 log base 5 of x+6- log base 5 of x-8- log base 5 of x-7	$3 \log_{5} (x + 6) - \log_{5} (x - 8) - \log_{5} (x - 7)$
23069	Simplify/Condense	3 log base 5 of x-3+1/2*( log base 5 of y-2 log base 5 of 2)	$3 \log_{5} (x - 3) + \frac{1}{2} \cdot (\log_{5} (y) - 2 \log_{5} (2))$
23070	Simplify/Condense	36 log of 2x-6 log of 2y	$36 \log (2) x - 6 \log (2) y$
23071	Simplify/Condense	37194-6106.73 natural log of 320	$37194 - 6106.73 \ln (320)$
23072	Simplify/Condense	38+(72-38)e^(-1/2 natural log of 17/11*7)	$38 + (72 - 38) \cdot e^{- \frac{1}{2} \cdot \ln (\frac{17}{11}) \cdot 7}$
23073	Simplify/Condense	3 natural log of B^e	$3 \ln (B^{e})$
23074	Simplify/Condense	3 log base 6 of x-8 log base 6 of y	$3 \log_{6} (x) - 8 \log_{6} (y)$
23075	Simplify/Condense	3 log base 6 of x+7- log base 6 of x-8- log base 6 of x-12	$3 \log_{6} (x + 7) - \log_{6} (x - 8) - \log_{6} (x - 12)$
23076	Simplify/Condense	3 log base 6 of x+8- log base 6 of x-12- log base 6 of x-3	$3 \log_{6} (x + 8) - \log_{6} (x - 12) - \log_{6} (x - 3)$
23077	Simplify/Condense	3 log base 7 of 2+1/2* log base 7 of 49	$3 \log_{7} (2) + \frac{1}{2} \cdot \log_{7} (49)$
23078	Simplify/Condense	3 log base 7 of 2+ log base 7 of 6	$3 \log_{7} (2) + \log_{7} (6)$
23079	Simplify/Condense	3 log base 7 of a+15 log base 7 of b	$3 \log_{7} (a) + 15 \log_{7} (b)$
23080	Simplify/Condense	3 log base 7 of u+8 log base 7 of v	$3 \log_{7} (u) + 8 \log_{7} (v)$
23081	Simplify/Condense	3 log base 7 of x-1/2* log base 7 of y+7 log base 7 of z	$3 \log_{7} (x) - \frac{1}{2} \cdot \log_{7} (y) + 7 \log_{7} (z)$
23082	Simplify/Condense	3 log base 7 of x+3 log base 7 of y-4 log base 7 of z	$3 \log_{7} (x) + 3 \log_{7} (y) - 4 \log_{7} (z)$
23083	Simplify/Condense	3 log base 7 of x+4 log base 7 of y-4 log base 7 of z	$3 \log_{7} (x) + 4 \log_{7} (y) - 4 \log_{7} (z)$
23084	Simplify/Condense	3 log base 8 of 2+3 log base 8 of x+15 log base 8 of y	$3 \log_{8} (2) + 3 \log_{8} (x) + 15 \log_{8} (y)$
23085	Simplify/Condense	3 log base 8 of 4+ log base 8 of 4+ log base 8 of 2	$3 \log_{8} (4) + \log_{8} (4) + \log_{8} (2)$
23086	Simplify/Condense	3 log base 8 of x-12 log base 8 of y	$3 \log_{8} (x) - 12 \log_{8} (y)$
23087	Simplify/Condense	-3 log base 9 of 4+ log base 9 of 1/8	$- 3 \log_{9} (4) + \log_{9} (\frac{1}{8})$
23088	Simplify/Condense	3 log base a of 4x^7-1/4* log base a of 6x+17	$3 \log_{a} (4 x^{7}) - \frac{1}{4} \cdot \log_{a} (6 x + 17)$
23089	Simplify/Condense	2 natural log of x+8-4 natural log of x	$2 \ln (x + 8) - 4 \ln (x)$
23090	Simplify/Condense	2 natural log of x-1-1/2* natural log of x- natural log of x-1	$2 \ln (x - 1) - \frac{1}{2} \cdot \ln (x) - \ln (x - 1)$
23091	Simplify/Condense	2 natural log of x-3 natural log of y+ natural log of z	$2 \ln (x - 3) \ln (y) + \ln (z)$
23092	Simplify/Condense	2 natural log of x-4 natural log of y	$2 \ln (x - 4) \ln (y)$
23093	Simplify/Condense	2 log of ( fourth root of m)/m+ log of square root of 100m^3	$2 \log (\frac{\sqrt[4]{m}}{m}) + \log (\sqrt{100 m^{3}})$
23094	Simplify/Condense	2 log of (y^3)/(x^3)-3 log of y+1/2* log of x^4y^2	$2 \log (\frac{y^{3}}{x^{3}}) - 3 \log (y) + \frac{1}{2} \cdot \log (x^{4} y^{2})$
23095	Simplify/Condense	2 log of (y^3)/x-3 log of y+1/2* log of x^4y^2	$2 \log (\frac{y^{3}}{x}) - 3 \log (y) + \frac{1}{2} \cdot \log (x^{4} y^{2})$
23096	Simplify/Condense	2 log of (y^4)/x-3 log of y+1/2* log of x^4y^2	$2 \log (\frac{y^{4}}{x}) - 3 \log (y) + \frac{1}{2} \cdot \log (x^{4} y^{2})$
23097	Simplify/Condense	2 log of square root of 6- log of 15x+ log of 7x+1	$2 \log (\sqrt{6}) - \log (15 x) + \log (7 x) + 1$
23098	Simplify/Condense	2 natural log of x- natural log of x-1+ natural log of x+1	$2 \ln (x) - \ln (x - 1) + \ln (x + 1)$
23099	Simplify/Condense	2 natural log of x-1/6 natural log of y	$2 \ln (x - \frac{1}{6}) \ln (y)$
23100	Simplify/Condense	2 natural log of x+1/2 natural log of x^2-1-1/2* natural log of x^(2+1)	$2 \ln (x + \frac{1}{2}) \ln (x^{2} - 1) - \frac{1}{2} \cdot \ln (x^{2 + 1})$