Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
22901	Simplify/Condense	2 log base 6 of 3+ log base 6 of 4	$2 \log_{6} (3) + \log_{6} (4)$
22902	Simplify/Condense	2 log base 6 of 3+3 log base 6 of 8-5 log base 6 of 11	$2 \log_{6} (3) + 3 \log_{6} (8) - 5 \log_{6} (11)$
22903	Simplify/Condense	2 log base 6 of 5-10 log base 6 of 7	$2 \log_{6} (5) - 10 \log_{6} (7)$
22904	Simplify/Condense	2- log base 6 of 5+x	$2 - \log_{6} (5 + x)$
22905	Simplify/Condense	2 log base 6 of 6y+1+1/2* log base 8 of y+3	$2 \log_{6} (6 y + 1) + \frac{1}{2} \cdot \log_{8} (y + 3)$
22906	Simplify/Condense	2 log base 6 of 8z+1+(1/4) log base 6 of z+3	$2 \log_{6} (8 z + 1) + (\frac{1}{4}) \log_{6} (z + 3)$
22907	Simplify/Condense	2 log base 6 of u-6 log base 6 of v	$2 \log_{6} (u) - 6 \log_{6} (v)$
22908	Simplify/Condense	2 log base 6 of x+6- log base 6 of x-19- log base 6 of x-2	$2 \log_{6} (x + 6) - \log_{6} (x - 19) - \log_{6} (x - 2)$
22909	Simplify/Condense	2 log base 7 of square root of 8x-1- log base 7 of 7/x+ log base 7 of 7	$2 \log_{7} (\sqrt{8 x - 1}) - \log_{7} (\frac{7}{x}) + \log_{7} (7)$
22910	Simplify/Condense	2 log base 7 of x^4-6 log base 7 of cube root of x^2+3 log base 7 of 4x+ log base 7 of 2	$2 \log_{7} (x^{4}) - 6 \log_{7} (\sqrt[3]{x^{2}}) + 3 \log_{7} (4 x) + \log_{7} (2)$
22911	Simplify/Condense	2 log base 7 of 3+1/4+1/4* log base 7 of x-5-1/2* log base 7 of x	$2 \log_{7} (3 + \frac{1}{4}) + \frac{1}{4} \cdot \log_{7} (x - 5) - \frac{1}{2} \cdot \log_{7} (x)$
22912	Simplify/Condense	2- log base 7 of 6-2 log base 7 of x	$2 - \log_{7} (6) - 2 \log_{7} (x)$
22913	Simplify/Condense	2 log base 7 of u+4 log base 7 of v	$2 \log_{7} (u) + 4 \log_{7} (v)$
22914	Simplify/Condense	2 log base 7 of x+3 log base 7 of y-3 log base 7 of z	$2 \log_{7} (x) + 3 \log_{7} (y) - 3 \log_{7} (z)$
22915	Simplify/Condense	2 log base 7 of y-1/3* log base 7 of w+3 log base 7 of z	$2 \log_{7} (y) - \frac{1}{3} \cdot \log_{7} (w) + 3 \log_{7} (z)$
22916	Simplify/Condense	2 log base 8 of 9x- log base 8 of 2x-5	$2 \log_{8} (9 x) - \log_{8} (2 x - 5)$
22917	Simplify/Condense	2 log base 8 of x+ log base 8 of y-3 log base 8 of z	$2 \log_{8} (x) + \log_{8} (y) - 3 \log_{8} (z)$
22918	Simplify/Condense	2 log base 9 of 11+( log base 9 of 2)/2	$2 \log_{9} (11) + \frac{\log_{9} (2)}{2}$
22919	Simplify/Condense	2 log base 2 of 15- log base 2 of 5+ log base 2 of 3	$2 \log_{2} (15) - \log_{2} (5) + \log_{2} (3)$
22920	Simplify/Condense	2 log base 2 of 2+2 log base 2 of 6- log base 2 of 3*2	$2 \log_{2} (2) + 2 \log_{2} (6) - \log_{2} (3 \cdot 2)$
22921	Simplify/Condense	2 log base 2 of 24- log base 2 of 3	$2 \log_{2} (24) - \log_{2} (3)$
22922	Simplify/Condense	2 log base 2 of x+4 log of 2y-5/4( log of 2(3x-2))+3/2-1/4( log of 2(2y+1))	$2 \log_{2} (x) + 4 \log (2) y - \frac{5}{4} \cdot (\log (2) (3 x - 2)) + \frac{3}{2} - \frac{1}{4} \cdot (\log (2) (2 y + 1))$
22923	Simplify/Condense	10 natural log of 10^6(3.2)	$10 \ln (10^{6} (3.2))$
22924	Simplify/Condense	12 log of 2-4 log of 3	$12 \log (2) - 4 \log (3)$
22925	Simplify/Condense	12 log of x+6 log of z	$12 \log (x + 6 \log (z))$
22926	Simplify/Condense	1-3 log base 3 of x	$1 - 3 \log_{3} (x)$
22927	Simplify/Condense	-1312+303 natural log of 9	$- 1312 + 303 \ln (9)$
22928	Simplify/Condense	14 log of seventh root of x	$14 \log (\sqrt[7]{x})$
22929	Simplify/Condense	14 log of m+2/5* log of n	$14 \log (m) + \frac{2}{5} \cdot \log (n)$
22930	Simplify/Condense	15e^( natural log of x^2)	$15 e^{\ln (x^{2})}$
22931	Simplify/Condense	15 log base 4 of fifth root of y	$15 \log_{4} (\sqrt[5]{y})$
22932	Simplify/Condense	15 log base 7 of fifth root of y	$15 \log_{7} (\sqrt[5]{y})$
22933	Simplify/Condense	15+2 log base 2 of x=31	$15 + 2 \log_{2} (x) = 31$
22934	Simplify/Condense	160* log of 2	$160 \cdot \log (2)$
22935	Simplify/Condense	160+10(-13.3)+10 log of 8	$160 + 10 (- 13.3) + 10 \log (8)$
22936	Simplify/Condense	18 log base 2 of square root of 3x-1- log base 2 of 9/x+ log base 2 of 9	$18 \log_{2} (\sqrt{3 x - 1}) - \log_{2} (\frac{9}{x}) + \log_{2} (9)$
22937	Simplify/Condense	18 log base 3 of cube root of x+ log base 3 of 18x^8- log base 3 of 18	$18 \log_{3} (\sqrt[3]{x}) + \log_{3} (18 x^{8}) - \log_{3} (18)$
22938	Simplify/Condense	1- log of x	$1 - \log (x)$
22939	Simplify/Condense	2 log base 7 of x-6+3 log base 7 of x+3	$2 \log_{7} (x - 6) + 3 \log_{7} (x + 3)$
22940	Simplify/Condense	2( log base 2 of 3+(1/2) log base 2 of x)- log base 2 of y-4 log base 2 of x	$2 (\log_{2} (3) + (\frac{1}{2}) \log_{2} (x)) - \log_{2} (y) - 4 \log_{2} (x)$
22941	Simplify/Condense	2( log base 3 of x+2 log base 3 of y-4 log base 3 of z)	$2 (\log_{3} (x) + 2 \log_{3} (y) - 4 \log_{3} (z))$
22942	Simplify/Condense	2( log base 5 of a+(1/2) log base 5 of d)-3 log base 5 of b-4 log base 5 of c	$2 (\log_{5} (a) + (\frac{1}{2}) \log_{5} (d)) - 3 \log_{5} (b) - 4 \log_{5} (c)$
22943	Simplify/Condense	2( log base 5 of x+2 log base 5 of y+3 log base 5 of z)	$2 (\log_{5} (x) + 2 \log_{5} (y) + 3 \log_{5} (z))$
22944	Simplify/Condense	2( log base 7 of x+3 log base 7 of y-5 log base 7 of z)	$2 (\log_{7} (x) + 3 \log_{7} (y) - 5 \log_{7} (z))$
22945	Simplify/Condense	2( log base b of w-4 log base b of y)+2 log base b of z	$2 (\log_{b} (w) - 4 \log_{b} (y)) + 2 \log_{b} (z)$
22946	Simplify/Condense	2( natural log of x-5+ natural log of y- natural log of x+y)	$2 (\ln (x - 5) + \ln (y) - \ln (x + y))$
22947	Simplify/Condense	2 log of 15	$2 \log (15)$
22948	Simplify/Condense	2 log of 3	$2 \log (3)$
22949	Simplify/Condense	2 log of 5+ log of 4	$2 \log (5) + \log (4)$
22950	Simplify/Condense	2 log of x+3 log of x+1	$2 \log (x) + 3 \log (x + 1)$
22951	Simplify/Condense	-2 log of x+5	$- 2 \log (x) + 5$
22952	Simplify/Condense	2( natural log of x- natural log of x+1+ natural log of x-1)	$2 (\ln (x) - \ln (x + 1) + \ln (x - 1))$
22953	Simplify/Condense	2( natural log of z+ natural log of z+2)-5 natural log of z-9	$2 (\ln (z) + \ln (z + 2)) - 5 \ln (z - 9)$
22954	Simplify/Condense	2( natural log of z+ natural log of z+7)-8 natural log of z-3	$2 (\ln (z) + \ln (z + 7)) - 8 \ln (z - 3)$
22955	Simplify/Condense	2e^(3 natural log of x+1)	$2 e^{3 \ln (x + 1)}$
22956	Simplify/Condense	-2 natural log of (e)^2+1	$- 2 \ln ({(e)}^{2}) + 1$
22957	Simplify/Condense	2 natural log of (e)^(3x)	$2 \ln ({(e)}^{3 x})$
22958	Simplify/Condense	(2( log of 3y^-1))/3	$\frac{2 (\log (3 y^{- 1}))}{3}$
22959	Simplify/Condense	(2( log of 7))/3	$\frac{2 (\log (7))}{3}$
22960	Simplify/Condense	12 log base 7 of 3+12 log base 7 of 11-3 log base 7 of 5	$12 \log_{7} (3) + 12 \log_{7} (11) - 3 \log_{7} (5)$
22961	Simplify/Condense	12 log base 8 of a+4 log base 8 of b	$12 \log_{8} (a) + 4 \log_{8} (b)$
22962	Simplify/Condense	2( log of 2x- log of y)-( log of 3+2 log of 5)	$2 (\log (2 x - \log (y))) - (\log (3) + 2 \log (5))$
22963	Simplify/Condense	2( log of z- log of 3)	$2 (\log (z) - \log (3))$
22964	Simplify/Condense	-2 log base 3 of 1/x+1/3*( log base 3 of square root of x)	$- 2 \log_{3} (\frac{1}{x}) + \frac{1}{3} \cdot (\log_{3} (\sqrt{x}))$
22965	Simplify/Condense	2 log base 3 of 12-6 log base 3 of 11	$2 \log_{3} (12) - 6 \log_{3} (11)$
22966	Simplify/Condense	2 log base 3 of 27-1/2* log base 3 of 9+1/3* log base 3 of 27^3- log base 3 of x	$2 \log_{3} (27) - \frac{1}{2} \cdot \log_{3} (9) + \frac{1}{3} \cdot \log_{3} (27^{3}) - \log_{3} (x)$
22967	Simplify/Condense	2 log base 3 of 4-4 log base 3 of 5	$2 \log_{3} (4) - 4 \log_{3} (5)$
22968	Simplify/Condense	2 log base 3 of 6-1/2* log base 3 of 400+3 log base 3 of 45^(1/3)	$2 \log_{3} (6) - \frac{1}{2} \cdot \log_{3} (400) + 3 \log_{3} (45^{\frac{1}{3}})$
22969	Simplify/Condense	2 log base 3 of 6- log base 3 of 4	$2 \log_{3} (6) - \log_{3} (4)$
22970	Simplify/Condense	2 log base 3 of 8- log base 3 of 2	$2 \log_{3} (8) - \log_{3} (2)$
22971	Simplify/Condense	2 log base 3 of 9	$2 \log_{3} (9)$
22972	Simplify/Condense	2 log base 3 of m+1/2* log base 3 of n-5 log base 3 of p	$2 \log_{3} (m) + \frac{1}{2} \cdot \log_{3} (n) - 5 \log_{3} (p)$
22973	Simplify/Condense	2 log base 3 of p-1/2* log base 3 of q	$2 \log_{3} (p) - \frac{1}{2} \cdot \log_{3} (q)$
22974	Find the Domain	g(x)=( square root of x)/(4x^2+3x-1)	$g (x) = \frac{\sqrt{x}}{4 x^{2} + 3 x - 1}$
22975	Simplify/Condense	2 log base 3 of x-1/2*( log base 3 of x+5 log base 3 of z)	$2 \log_{3} (x) - \frac{1}{2} \cdot (\log_{3} (x) + 5 \log_{3} (z))$
22976	Simplify/Condense	2 log base 3 of x+6 log base 3 of y-5 log base 3 of z	$2 \log_{3} (x) + 6 \log_{3} (y) - 5 \log_{3} (z)$
22977	Simplify/Condense	2 log base 3 of x+9- log base 3 of x-10- log base 3 of x-13	$2 \log_{3} (x + 9) - \log_{3} (x - 10) - \log_{3} (x - 13)$
22978	Simplify/Condense	2 log base 3 of x-7	$2 \log_{3} (x - 7)$
22979	Simplify/Condense	2 log base 4 of 2x+0.5 log base 4 of x+3- log base 4 of x^2-9	$2 \log_{4} (2 x) + 0.5 \log_{4} (x + 3) - \log_{4} (x^{2} - 9)$
22980	Simplify/Condense	2 log base 4 of 3-1/2* log base 4 of x	$2 \log_{4} (3) - \frac{1}{2} \cdot \log_{4} (x)$
22981	Simplify/Condense	2 log base 4 of 7+( log base 4 of 8)/2	$2 \log_{4} (7) + \frac{\log_{4} (8)}{2}$
22982	Simplify/Condense	2 log base 4 of 8- log base 4 of 3	$2 \log_{4} (8) - \log_{4} (3)$
22983	Simplify/Condense	2 log of x-5 log of x-4	$2 \log (x - 5) \log (x - 4)$
22984	Simplify/Condense	12.5e^( natural log of 2*7)	$12.5 e^{\ln (2) \cdot 7}$
22985	Simplify/Condense	12 log of x	$12 \log (x)$
22986	Simplify/Condense	12 log base 12 of 6	$12 \log_{12} (6)$
22987	Simplify/Condense	2 log base 2 of 3	$2 \log_{2} (3)$
22988	Simplify/Condense	2 log base 2 of 3- log base 2 of 72	$2 \log_{2} (3) - \log_{2} (72)$
22989	Simplify/Condense	2 log base 2 of 7	$2 \log_{2} (7)$
22990	Simplify/Condense	2 log base 2 of 7+7 log base 2 of 4	$2 \log_{2} (7) + 7 \log_{2} (4)$
22991	Simplify/Condense	2 log base 2 of 9	$2 \log_{2} (9)$
22992	Simplify/Condense	2 log base 2 of x- log base 2 of 3+3 log base 2 of x	$2 \log_{2} (x) - \log_{2} (3) + 3 \log_{2} (x)$
22993	Simplify/Condense	2 log base 2 of x- log base 2 of x-2	$2 \log_{2} (x) - \log_{2} (x - 2)$
22994	Simplify/Condense	2 log base 2 of x+1/3*( log of 2(27x-27))-2 log base 2 of x^3-x	$2 \log_{2} (x) + \frac{1}{3} \cdot (\log (2) (27 x - 27)) - 2 \log_{2} (x^{3} - x)$
22995	Simplify/Condense	2 log base 2 of x+ log base 2 of xy	$2 \log_{2} (x) + \log_{2} (x y)$
22996	Simplify/Condense	2 log base 4 of A+2 log base 4 of B-2 log base 4 of c	$2 \log_{4} (A) + 2 \log_{4} (B) - 2 \log_{4} (c)$
22997	Simplify/Condense	2 log base 4 of A+5 log base 4 of B-3 log base 4 of C	$2 \log_{4} (A) + 5 \log_{4} (B) - 3 \log_{4} (C)$
22998	Simplify/Condense	2 log base 4 of m+6 log base 4 of n	$2 \log_{4} (m) + 6 \log_{4} (n)$
22999	Simplify/Condense	2 log base 4 of x- log base 4 of y- log base 4 of z	$2 \log_{4} (x) - \log_{4} (y) - \log_{4} (z)$
23000	Simplify/Condense	2 log base 5 of square root of 6x-1- log base 5 of 6/x+ log base 5 of 6	$2 \log_{5} (\sqrt{6 x - 1}) - \log_{5} (\frac{6}{x}) + \log_{5} (6)$