Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
21901	Simplify/Condense	1/3* log of a	$\frac{1}{3} \cdot \log (a)$
21902	Simplify/Condense	1/3* log base 2 of a+ log base 2 of b+1	$\frac{1}{3} \cdot \log_{2} (a) + \log_{2} (b + 1)$
21903	Simplify/Condense	1/3* log base 3 of x^6+1/6* log base 3 of x^6-1/9* log base 3 of x	$\frac{1}{3} \cdot \log_{3} (x^{6}) + \frac{1}{6} \cdot \log_{3} (x^{6}) - \frac{1}{9} \cdot \log_{3} (x)$
21904	Simplify/Condense	1/3* log base 3 of 9	$\frac{1}{3} \cdot \log_{3} (9)$
21905	Simplify/Condense	1/3* log base 3 of w+4 log base 3 of z- log base 3 of x	$\frac{1}{3} \cdot \log_{3} (w) + 4 \log_{3} (z) - \log_{3} (x)$
21906	Simplify/Condense	1/3* log base 3 of z+2 log base 3 of w- log base 3 of y	$\frac{1}{3} \cdot \log_{3} (z) + 2 \log_{3} (w) - \log_{3} (y)$
21907	Simplify/Condense	1/3( log base 5 of p1)/4* log base 5 of q-2 log base 5 of t	$\frac{1}{3} \cdot \frac{\log_{5} (p) \cdot 1}{4} \cdot \log_{5} (q) - 2 \log_{5} (t)$
21908	Simplify/Condense	1/3* log base 6 of a-2 log base 6 of b+5 log base 6 of c	$\frac{1}{3} \cdot \log_{6} (a - 2 \log_{6} (b) + 5 \log_{6} (c))$
21909	Simplify/Condense	1/3* log base 6 of x+7 log base 6 of y- log base 6 of z	$\frac{1}{3} \cdot \log_{6} (x) + 7 \log_{6} (y) - \log_{6} (z)$
21910	Simplify/Condense	1/3* log base 8 of x+2+7 log base 8 of x	$\frac{1}{3} \cdot \log_{8} (x + 2) + 7 \log_{8} (x)$
21911	Simplify/Condense	1/3* log base b of x^4y^5-3/4* log base b of x^2y	$\frac{1}{3} \cdot \log_{b} (x^{4} y^{5}) - \frac{3}{4} \cdot \log_{b} (x^{2} y)$
21912	Simplify/Condense	1/3* log base b of 27-5 log base b of 2+ log base b of 11	$\frac{1}{3} \cdot \log_{b} (27) - 5 \log_{b} (2) + \log_{b} (11)$
21913	Simplify/Condense	1/3* log base b of x+3 log base b of y-5 log base b of x	$\frac{1}{3} \cdot \log_{b} (x) + 3 \log_{b} (y) - 5 \log_{b} (x)$
21914	Simplify/Condense	1/3* log base c of x+4 log base c of y-5 log base c of x	$\frac{1}{3} \cdot \log_{c} (x) + 4 \log_{c} (y) - 5 \log_{c} (x)$
21915	Simplify/Condense	1/3*( log base c of x+4 log base c of y-2 log base c of x)	$\frac{1}{3} \cdot (\log_{c} (x + 4) \log_{c} (y - 2) \log_{c} (x))$
21916	Simplify/Condense	1/3* log base m of z+4 log base m of x- log base m of w	$\frac{1}{3} \cdot \log_{m} (z) + 4 \log_{m} (x) - \log_{m} (w)$
21917	Simplify/Condense	1/3* log base x of 8+2 log base x of 6- log base x of 3	$\frac{1}{3} \cdot \log_{x} (8) + 2 \log_{x} (6) - \log_{x} (3)$
21918	Simplify/Condense	1/3* natural log of w-3 natural log of x-5 natural log of y	$\frac{1}{3} \cdot \ln (w) - 3 \ln (x) - 5 \ln (y)$
21919	Simplify/Condense	1/3*( natural log of x-2+2 natural log of x+2- natural log of x+2-5 natural log of x-1)	$\frac{1}{3} \cdot (\ln (x - 2) + 2 \ln (x + 2) - \ln (x + 2) - 5 \ln (x - 1))$
21920	Simplify/Condense	1/3* natural log of x+2+1/2*( natural log of xx- natural log of x^2+3x+2)	$\frac{1}{3} \cdot \ln (x + 2) + \frac{1}{2} \cdot (\ln (x) x - \ln (x^{2} + 3 x + 2))$
21921	Simplify/Condense	1/3*( log base 2 of a^5- log base 2 of bc^3)	$\frac{1}{3} \cdot (\log_{2} (a^{5}) - \log_{2} (b c^{3}))$
21922	Simplify/Condense	1/3*( log base 4 of x- log base 4 of y)	$\frac{1}{3} \cdot (\log_{4} (x) - \log_{4} (y))$
21923	Simplify/Condense	1/3*( log base 4 of x- log base 4 of y+2 log base 4 of x+1)	$\frac{1}{3} \cdot (\log_{4} (x) - \log_{4} (y) + 2 \log_{4} (x + 1))$
21924	Simplify/Condense	1/3*(2 natural log of x+3 natural log of x- natural log of x^2-1)	$\frac{1}{3} \cdot (2 \ln (x + 3) \ln (x) - \ln (x^{2} - 1))$
21925	Simplify/Condense	1/3*(5 natural log of x+6- natural log of x- natural log of x^2-25)	$\frac{1}{3} \cdot (5 \ln (x + 6) - \ln (x - \ln (x^{2}) - 25))$
21926	Simplify/Condense	1/3*( natural log of 3+5 natural log of x- natural log of y)	$\frac{1}{3} \cdot (\ln (3 + 5 \ln (x - \ln (y))))$
21927	Simplify/Condense	1/3*( natural log of 4- natural log of 32)	$\frac{1}{3} \cdot (\ln (4) - \ln (32))$
21928	Simplify/Condense	1/3*( log of a^2+ log of b- log of c)	$\frac{1}{3} \cdot (\log (a^{2}) + \log (b) - \log (c))$
21929	Simplify/Condense	1/3*( log of m- log of n)	$\frac{1}{3} \cdot (\log (m) - \log (n))$
21930	Simplify/Condense	1/3*( log of t- log of t+1)- log of t-1	$\frac{1}{3} \cdot (\log (t) - \log (t + 1)) - \log (t - 1)$
21931	Simplify/Condense	1/3*( log of x-2 log of y+3 log of z)	$\frac{1}{3} \cdot (\log (x - 2) \log (y + 3) \log (z))$
21932	Simplify/Condense	1/3*(2 natural log of x+6- natural log of x- natural log of x^2-36)	$\frac{1}{3} \cdot (2 \ln (x + 6) - \ln (x) - \ln (x^{2} - 36))$
21933	Simplify/Condense	1/3*( log base 3 of x+ log base 3 of 7)-( log base 3 of y)	$\frac{1}{3} \cdot (\log_{3} (x) + \log_{3} (7)) - (\log_{3} (y))$
21934	Simplify/Condense	1/2*( log of x+4 log of x-1)	$\frac{1}{2} \cdot (\log (x + 4) \log (x - 1))$
21935	Simplify/Condense	1/25* log of 7.41+70 log of 2472	$\frac{1}{25} \cdot \log (7.41) + 70 \log (2472)$
21936	Simplify/Condense	1/2* log of x- log of 9y+ log of 2z	$\frac{1}{2} \cdot \log (x) - \log (9 y) + \log (2 z)$
21937	Simplify/Condense	1/2* log of x- log of y+ log of 3z	$\frac{1}{2} \cdot \log (x) - \log (y) + \log (3 z)$
21938	Simplify/Condense	1/2* log of x- log of y+ log of z	$\frac{1}{2} \cdot \log (x) - \log (y) + \log (z)$
21939	Simplify/Condense	1/3*( log base 9 of x+4+3 log base 9 of x-4)+6 log base 9 of x	$\frac{1}{3} \cdot (\log_{9} (x + 4) + 3 \log_{9} (x - 4)) + 6 \log_{9} (x)$
21940	Simplify/Condense	1/3*(2h(x+3)+ natural log of x- natural log of x^2-1)	$\frac{1}{3} \cdot (2 h (x + 3) + \ln (x) - \ln (x^{2} - 1))$
21941	Simplify/Condense	1/2* natural log of x-2 natural log of y	$\frac{1}{2} \cdot \ln (x) - 2 \ln (y)$
21942	Simplify/Condense	1/2* natural log of x- natural log of 2	$\frac{1}{2} \cdot \ln (x) - \ln (2)$
21943	Simplify/Condense	1/3*(5- natural log of x- natural log of x^2-25)	$\frac{1}{3} \cdot (5 - \ln (x) - \ln (x^{2} - 25))$
21944	Simplify/Condense	1/2*( log base 4 of x+1+2 log base 4 of x-1+6 log base 4 of x)	$\frac{1}{2} \cdot (\log_{4} (x + 1) + 2 \log_{4} (x - 1) + 6 \log_{4} (x))$
21945	Simplify/Condense	1/2*( natural log of x-4+5 natural log of x^2+4x)	$\frac{1}{2} \cdot (\ln (x - 4) + 5 \ln (x^{2} + 4 x))$
21946	Simplify/Condense	1/2*e^( natural log of 3-2 natural log of 5)	$\frac{1}{2} \cdot e^{\ln (3) - 2 \ln (5)}$
21947	Simplify/Condense	1/2*( log base 8 of x+ log base 8 of y)-6 log base 8 of x+6	$\frac{1}{2} \cdot (\log_{8} (x) + \log_{8} (y)) - 6 \log_{8} (x + 6)$
21948	Simplify/Condense	1/2*( log base 9 of x+ log base 9 of y)-5 log base 9 of x+9	$\frac{1}{2} \cdot (\log_{9} (x) + \log_{9} (y)) - 5 \log_{9} (x + 9)$
21949	Simplify/Condense	1/2*( log base 9 of x+ log base 9 of y-3 log base 9 of x+9)	$\frac{1}{2} \cdot (\log_{9} (x) + \log_{9} (y) - 3 \log_{9} (x + 9))$
21950	Simplify/Condense	1/2*( log base b of M+ log base b of N- log base b of P)	$\frac{1}{2} \cdot (\log_{b} (M) + \log_{b} (N) - \log_{b} (P))$
21951	Simplify/Condense	1/2*( natural log of x+ natural log of 4- natural log of 9)	$\frac{1}{2} \cdot (\ln (x) + \ln (4) - \ln (9))$
21952	Simplify/Condense	1/2*( log base 5 of x+ log base 5 of y)-3 log base 5 of x+7	$\frac{1}{2} \cdot (\log_{5} (x) + \log_{5} (y)) - 3 \log_{5} (x + 7)$
21953	Simplify/Condense	1/2*( log base 6 of s+ log base 6 of t)	$\frac{1}{2} \cdot (\log_{6} (s) + \log_{6} (t))$
21954	Simplify/Condense	1/2*( log base 6 of x+ log base 6 of y-6 log base 6 of x+3)	$\frac{1}{2} \cdot (\log_{6} (x + \log_{6} (y) - 6 \log_{6} (x + 3)))$
21955	Simplify/Condense	1/2*( log base 7 of a+ log base 7 of b)	$\frac{1}{2} \cdot (\log_{7} (a) + \log_{7} (b))$
21956	Simplify/Condense	1/2*( log base 7 of x+ log base 7 of y-6 log base 7 of x+6)	$\frac{1}{2} \cdot (\log_{7} (x) + \log_{7} (y) - 6 \log_{7} (x + 6))$
21957	Simplify/Condense	1/2*( log base 7 of x+4+2 log base 7 of x-7)+8 log base 7 of x	$\frac{1}{2} \cdot (\log_{7} (x + 4) + 2 \log_{7} (x - 7)) + 8 \log_{7} (x)$
21958	Simplify/Condense	1/2*(( natural log of 10/3)/( natural log of 4)+1)	$\frac{1}{2} \cdot (\frac{\ln (\frac{10}{3})}{\ln (4)} + 1)$
21959	Simplify/Condense	1/2*( log base 4 of x+1+2 log base 2 of x-1)+6 log base 4 of x	$\frac{1}{2} \cdot (\log_{4} (x + 1) + 2 \log_{2} (x - 1)) + 6 \log_{4} (x)$
21960	Simplify/Condense	1/2* log base 2 of 3x1/3 log base 2 of 4x	$\frac{1}{2} \cdot \log_{2} (3 x) \cdot \frac{1}{3} \cdot \log_{2} (4 x)$
21961	Simplify/Condense	1/2* log base 2 of x+ log base 2 of y	$\frac{1}{2} \cdot \log_{2} (x) + \log_{2} (y)$
21962	Simplify/Condense	1/2* log base 2 of x+1- log base 2 of y+2 log base 2 of z	$\frac{1}{2} \cdot \log_{2} (x + 1) - \log_{2} (y) + 2 \log_{2} (z)$
21963	Simplify/Condense	1/2* log base 3 of 144-2 log base 3 of 6	$\frac{1}{2} \cdot \log_{3} (144) - 2 \log_{3} (6)$
21964	Simplify/Condense	1/2* log base 3 of 81+ log base 3 of 15	$\frac{1}{2} \cdot \log_{3} (81) + \log_{3} (15)$
21965	Simplify/Condense	1/2* log base 6 of x+ log base 3 of y-6 log base 3 of x+7	$\frac{1}{2} \cdot \log_{6} (x) + \log_{3} (y) - 6 \log_{3} (x + 7)$
21966	Simplify/Condense	1/2* log base 6 of x+ log base 6 of y-3 log base 6 of z	$\frac{1}{2} \cdot \log_{6} (x) + \log_{6} (y) - 3 \log_{6} (z)$
21967	Simplify/Condense	1/2* log base 6 of x+7 log base 6 of 7- log base 6 of w	$\frac{1}{2} \cdot \log_{6} (x) + 7 \log_{6} (7) - \log_{6} (w)$
21968	Simplify/Condense	1/2* log base 7 of 9-3 log base 7 of x+2 log base 7 of y	$\frac{1}{2} \cdot \log_{7} (9) - 3 \log_{7} (x) + 2 \log_{7} (y)$
21969	Simplify/Condense	1/2* log base 7 of w+3 log base 7 of y- log base 7 of x	$\frac{1}{2} \cdot \log_{7} (w) + 3 \log_{7} (y) - \log_{7} (x)$
21970	Simplify/Condense	1/2* log base 8 of x-3 log base 8 of x+1	$\frac{1}{2} \cdot \log_{8} (x) - 3 \log_{8} (x + 1)$
21971	Simplify/Condense	1/2*( log base 3 of x+1/7 log base 3 of y-3 log base 3 of w-(1/2) log base 3 of z)	$\frac{1}{2} \cdot (\log_{3} (x + \frac{1}{7}) \log_{3} (y - 3) \log_{3} (w - (\frac{1}{2})) \log_{3} (z))$
21972	Simplify/Condense	1/2* log base 3 of x-1+4 log base 3 of x+2-5 log base 3 of y	$\frac{1}{2} \cdot \log_{3} (x - 1) + 4 \log_{3} (x + 2) - 5 \log_{3} (y)$
21973	Simplify/Condense	1/2* log base 4 of x-3 log base 4 of y- log base 4 of z	$\frac{1}{2} \cdot \log_{4} (x) - 3 \log_{4} (y) - \log_{4} (z)$
21974	Simplify/Condense	1/2* log base 5 of 49-1/3* log base 5 of 8+13 log base 5 of 1	$\frac{1}{2} \cdot \log_{5} (49) - \frac{1}{3} \cdot \log_{5} (8) + 13 \log_{5} (1)$
21975	Simplify/Condense	1/2* natural log of 3-1/2* natural log of 5	$\frac{1}{2} \cdot \ln (3) - \frac{1}{2} \cdot \ln (5)$
21976	Simplify/Condense	1/2* natural log of 36+2 natural log of 4- natural log of 4	$\frac{1}{2} \cdot \ln (36) + 2 \ln (4) - \ln (4)$
21977	Simplify/Condense	1/2* natural log of 5	$\frac{1}{2} \cdot \ln (5)$
21978	Simplify/Condense	1/2* natural log of 6	$\frac{1}{2} \cdot \ln (6)$
21979	Simplify/Condense	1/2* natural log of 9	$\frac{1}{2} \cdot \ln (9)$
21980	Simplify/Condense	1/2* natural log of 9+1/3* natural log of 64	$\frac{1}{2} \cdot \ln (9) + \frac{1}{3} \cdot \ln (64)$
21981	Simplify/Condense	1/2* natural log of x+4 natural log of y-5 natural log of z	$\frac{1}{2} \cdot \ln (x) + 4 \ln (y) - 5 \ln (z)$
21982	Simplify/Condense	1/2* natural log of x^2+1-4 natural log of 1/2-1/2*( natural log of x-4 natural log of x)	$\frac{1}{2} \cdot \ln (x^{2} + 1) - 4 \ln (\frac{1}{2}) - \frac{1}{2} \cdot (\ln (x - 4) \ln (x))$
21983	Simplify/Condense	1/2* natural log of 12	$\frac{1}{2} \cdot \ln (12)$
21984	Simplify/Condense	1/2* natural log of 25- natural log of 2	$\frac{1}{2} \cdot \ln (25) - \ln (2)$
21985	Simplify/Condense	1/2* log base a of x+3 log base a of y-4 log base a of x	$\frac{1}{2} \cdot \log_{a} (x) + 3 \log_{a} (y) - 4 \log_{a} (x)$
21986	Simplify/Condense	1/2* log base b of 16-2 log base b of 5	$\frac{1}{2} \cdot \log_{b} (16 - 2 \log_{b} (5))$
21987	Simplify/Condense	-1/2* log base r of square root of 3	$- \frac{1}{2} \cdot \log_{r} (\sqrt{3})$
21988	Simplify/Condense	1/2* log of x+3/2* log of y-2 log of x+2	$\frac{1}{2} \cdot \log (x) + \frac{3}{2} \cdot \log (y) - 2 \log (x + 2)$
21989	Simplify/Condense	1/2*( log of 7^s+ log of 7^t)	$\frac{1}{2} \cdot (\log (7^{s} + \log (7^{t})))$
21990	Simplify/Condense	1/2*( log of 4+2 log of 3-( log of 2+ log of 3))	$\frac{1}{2} \cdot (\log (4) + 2 \log (3) - (\log (2) + \log (3)))$
21991	Simplify/Condense	natural log of 7- natural log of 4- natural log of 8	$\ln (7) - \ln (4) - \ln (8)$
21992	Simplify/Condense	1/2*( log of b+5 log of c)	$\frac{1}{2} \cdot (\log (b + 5) \log (c))$
21993	Simplify/Condense	1/2*( log of b+7 log of c)	$\frac{1}{2} \cdot (\log (b + 7) \log (c))$
21994	Simplify/Condense	1/2* log of c+6 log of d	$\frac{1}{2} \cdot \log (c) + 6 \log (d)$
21995	Simplify/Condense	1/2* log of c+9 log of d	$\frac{1}{2} \cdot \log (c) + 9 \log (d)$
21996	Simplify/Condense	1/2* log of w+2 log of z- log of y	$\frac{1}{2} \cdot \log (w) + 2 \log (z) - \log (y)$
21997	Simplify/Condense	1/2* log of w-2 log of z	$\frac{1}{2} \cdot \log (w) - 2 \log (z)$
21998	Simplify/Condense	1/2* natural log of x- natural log of 4	$\frac{1}{2} \cdot \ln (x) - \ln (4)$
21999	Simplify/Condense	1/2* natural log of x- natural log of 7	$\frac{1}{2} \cdot \ln (x) - \ln (7)$
22000	Simplify/Condense	1/2* natural log of x- natural log of 8	$\frac{1}{2} \cdot \ln (x) - \ln (8)$