Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
21801	Simplify/Condense	2/3* natural log of y+ natural log of 3	$\frac{2}{3} \cdot \ln (y) + \ln (3)$
21802	Simplify/Condense	2/3* log of 4.34*(10^8)/(10^4.4)	$\frac{2}{3} \cdot \log (4.34 \cdot \frac{10^{8}}{10^{4.4}})$
21803	Simplify/Condense	2^(\| log base 2 of 9\|)	$2^{\| \log_{2} (9) \|}$
21804	Simplify/Condense	2^( log base 2 of 16)	$2^{\log_{2} (16)}$
21805	Simplify/Condense	1000^( log of x)	$1000^{\log (x)}$
21806	Simplify/Condense	1000^(3 log of x^3)	$1000^{3 \log (x^{3})}$
21807	Simplify/Condense	1000^(3 log of x^4)	$1000^{3 \log (x^{4})}$
21808	Simplify/Condense	10000000/( log of x)	$\frac{10000000}{\log (x)}$
21809	Simplify/Condense	(10 natural log of 2)/(2 natural log of 2-9 natural log of 3)	$\frac{10 \ln (2)}{2 \ln (2) - 9 \ln (3)}$
21810	Simplify/Condense	11^(2 log of 11^3+ log of 11^2)	$11^{2 \log (11^{3} + \log (11^{2}))}$
21811	Simplify/Condense	12^( log base 12 of 144)	$12^{\log_{12} (144)}$
21812	Simplify/Condense	12^( log of 12*24)	$12^{\log (12) \cdot 24}$
21813	Simplify/Condense	13/6* log base 2 of z-3	$\frac{13}{6} \cdot \log_{2} (z - 3)$
21814	Simplify/Condense	2/3* log base 128 of 64+3/4* log base 128 of 16	$\frac{2}{3} \cdot \log_{128} (64) + \frac{3}{4} \cdot \log_{128} (16)$
21815	Simplify/Condense	2/3* log base 3 of x^3- log base 3 of 3/4y^4- log base 3 of 10	$\frac{2}{3} \cdot \log_{3} (x^{3}) - \log_{3} (\frac{3}{4} y^{4}) - \log_{3} (10)$
21816	Simplify/Condense	2/3* log base 5 of x-(4/5* log base 5 of y)-(5/2* log base 5 of z)	$\frac{2}{3} \cdot \log_{5} (x) - (\frac{4}{5} \cdot \log_{5} (y)) - (\frac{5}{2} \cdot \log_{5} (z))$
21817	Simplify/Condense	1/7+ natural log of 7	$\frac{1}{7} + \ln (7)$
21818	Simplify/Condense	1/7*( log base 7 of z+4 log base 7 of y)	$\frac{1}{7} \cdot (\log_{7} (z) + 4 \log_{7} (y))$
21819	Simplify/Condense	1/7*(3 natural log of x+6- natural log of x- natural log of x^2-25)	$\frac{1}{7} \cdot (3 \ln (x + 6) - \ln (x) - \ln (x^{2} - 25))$
21820	Simplify/Condense	1/5* log of z	$\frac{1}{5} \cdot \log (z)$
21821	Simplify/Condense	1/(5 log of 25)	$\frac{1}{5 \log (25)}$
21822	Simplify/Condense	1/6*( log base 2 of x+ log base 2 of y)	$\frac{1}{6} \cdot (\log_{2} (x) + \log_{2} (y))$
21823	Simplify/Condense	1/6*(5 natural log of x+5- natural log of x- natural log of x^2-4)	$\frac{1}{6} \cdot (5 \ln (x + 5) - \ln (x) - \ln (x^{2} - 4))$
21824	Simplify/Condense	1/6-( natural log of 3)/6	$\frac{1}{6} - \frac{\ln (3)}{6}$
21825	Simplify/Condense	1/5* log of (x+3)^5+1/3*( log of x^6- log of (x^2-x-12)^3)	$\frac{1}{5} \cdot \log ({(x + 3)}^{5}) + \frac{1}{3} \cdot (\log (x^{6}) - \log ({(x^{2} - x - 12)}^{3}))$
21826	Simplify/Condense	1/5* log base 4 of 16	$\frac{1}{5} \cdot \log_{4} (16)$
21827	Simplify/Condense	1/5* log base 7 of x^2- log base 7 of pq	$\frac{1}{5} \cdot \log_{7} (x^{2}) - \log_{7} (p q)$
21828	Simplify/Condense	1/5* log base b of x^2y^6-5/7* log base b of x^6y	$\frac{1}{5} \cdot \log_{b} (x^{2} y^{6}) - \frac{5}{7} \cdot \log_{b} (x^{6} y)$
21829	Simplify/Condense	1/5* log base x of 32-3 log base x of 2+ log base x of 4	$\frac{1}{5} \cdot \log_{x} (32) - 3 \log_{x} (2) + \log_{x} (4)$
21830	Simplify/Condense	1/5* natural log of 2+1/2	$\frac{1}{5} \cdot \ln (2 + \frac{1}{2})$
21831	Simplify/Condense	1/5* natural log of 2+3	$\frac{1}{5} \cdot \ln (2 + 3)$
21832	Simplify/Condense	1/5* natural log of x	$\frac{1}{5} \cdot \ln (x)$
21833	Simplify/Condense	1/5* natural log of x+2/5* natural log of z-2 natural log of y	$\frac{1}{5} \cdot \ln (x) + \frac{2}{5} \cdot \ln (z) - 2 \ln (y)$
21834	Simplify/Condense	1/5* natural log of x+2/5* natural log of z- natural log of y	$\frac{1}{5} \cdot \ln (x) + \frac{2}{5} \cdot \ln (z) - \ln (y)$
21835	Simplify/Condense	1/5* log of 3^32-2 log of 3^x+1/2* log of 3^y	$\frac{1}{5} \cdot \log (3^{32}) - 2 \log (3^{x}) + \frac{1}{2} \cdot \log (3^{y})$
21836	Simplify/Condense	1/5* log of a^5-12 log of b+ log of c^12- log of d	$\frac{1}{5} \cdot \log (a^{5}) - 12 \log (b) + \log (c^{12}) - \log (d)$
21837	Simplify/Condense	1/5* log of 5x+1+1/3*( log of x-2- log of x^4-x^2-5)	$\frac{1}{5} \cdot \log (5 x + 1) + \frac{1}{3} \cdot (\log (x - 2) - \log (x^{4} - x^{2} - 5))$
21838	Simplify/Condense	1/5( log of 9p)+1/8( log base 9 of q-2 log base 9 of t)	$\frac{1}{5} \cdot (\log (9) p) + \frac{1}{8} \cdot (\log_{9} (q - 2) \log_{9} (t))$
21839	Simplify/Condense	1/8* natural log of y+ natural log of z	$\frac{1}{8} \cdot \ln (y + \ln (z))$
21840	Simplify/Condense	1/9*( log base 5 of z+4 log base 5 of y)	$\frac{1}{9} \cdot (\log_{5} (z) + 4 \log_{5} (y))$
21841	Simplify/Condense	1/9* log base 9 of 81	$\frac{1}{9} \cdot \log_{9} (81)$
21842	Simplify/Condense	10^(( log of 1.625)/6)-1	$10^{\frac{\log (1.625)}{6}} - 1$
21843	Simplify/Condense	10^( log of (10)^(6^2))	$10^{\log ({(10)}^{6^{2}})}$
21844	Simplify/Condense	10^(5 log of x)	$10^{5 \log (x)}$
21845	Simplify/Condense	10^( log of 10^17)*9	$10^{\log (10^{17})} \cdot 9$
21846	Simplify/Condense	1/8*( log base 7 of z+3 log base 7 of y)	$\frac{1}{8} \cdot (\log_{7} (z) + 3 \log_{7} (y))$
21847	Simplify/Condense	1/8*(3 natural log of x+6)- natural log of x- natural log of x^2-49	$\frac{1}{8} \cdot (3 \ln (x + 6)) - \ln (x) - \ln (x^{2} - 49)$
21848	Simplify/Condense	1/8* log base 3 of 2a	$\frac{1}{8} \cdot \log_{3} (2 a)$
21849	Simplify/Condense	10^( log of 53)	$10^{\log (53)}$
21850	Simplify/Condense	10^( log of 5x)	$10^{\log (5 x)}$
21851	Simplify/Condense	10^( log of x/(10^-12))	$10^{\log (\frac{x}{10^{- 12}})}$
21852	Simplify/Condense	10^( log of x^18)	$10^{\log (x^{18})}$
21853	Simplify/Condense	10^( log of 15)	$10^{\log (15)}$
21854	Simplify/Condense	1/4* log of 2x+y- log of 3x+2y	$\frac{1}{4} \cdot \log (2 x + y) - \log (3 x + 2 y)$
21855	Simplify/Condense	1/4* log of 3x+1-3 log of t	$\frac{1}{4} \cdot \log (3 x + 1) - 3 \log (t)$
21856	Simplify/Condense	1/4* log of 81+ log of 6- log of 5	$\frac{1}{4} \cdot \log (81) + \log (6) - \log (5)$
21857	Simplify/Condense	1/4* log of a-3 log of b+7 log of c+9 log of b	$\frac{1}{4} \cdot \log (a) - 3 \log (b) + 7 \log (c) + 9 \log (b)$
21858	Simplify/Condense	1/4* log of x+5 log of y-2 log of x	$\frac{1}{4} \cdot \log (x) + 5 \log (y) - 2 \log (x)$
21859	Simplify/Condense	1/(5 log base 6 of x+ log base 6 of 7- log base 6 of y)	$\frac{1}{5 \log_{6} (x) + \log_{6} (7) - \log_{6} (y)}$
21860	Simplify/Condense	1/5*( log base 4 of x+ log base 4 of 7)- log base 4 of y	$\frac{1}{5} \cdot (\log_{4} (x) + \log_{4} (7)) - \log_{4} (y)$
21861	Simplify/Condense	1/5*( log base 9 of z+2 log base 9 of y)	$\frac{1}{5} \cdot (\log_{9} (z) + 2 \log_{9} (y))$
21862	Simplify/Condense	1/5*(3 log base b of x-4 log base b of y)	$\frac{1}{5} \cdot (3 \log_{b} (x) - 4 \log_{b} (y))$
21863	Simplify/Condense	1/5*( log base 3 of x)+ log base 3 of 7-2 log base 4 of y-3	$\frac{1}{5} \cdot (\log_{3} (x)) + \log_{3} (7) - 2 \log_{4} (y - 3)$
21864	Simplify/Condense	1/5*( log base 5 of x+ log base 5 of y)	$\frac{1}{5} \cdot (\log_{5} (x) + \log_{5} (y))$
21865	Simplify/Condense	1/5*(2 natural log of x+5- natural log of x- natural log of x^2-49)	$\frac{1}{5} \cdot (2 \ln (x + 5) - \ln (x) - \ln (x^{2} - 49))$
21866	Simplify/Condense	1/3* log of 27-1/2* log of 64	$\frac{1}{3} \cdot \log (27) - \frac{1}{2} \cdot \log (64)$
21867	Simplify/Condense	1/3* log of 27x^2-3 log of y+ log of z	$\frac{1}{3} \cdot \log (27 x^{2}) - 3 \log (y) + \log (z)$
21868	Simplify/Condense	1/3* log of 2x+1+1/2*( log of x-4- log of x^4-x^2-1)	$\frac{1}{3} \cdot \log (2 x + 1) + \frac{1}{2} \cdot (\log (x - 4) - \log (x^{4} - x^{2} - 1))$
21869	Simplify/Condense	1/3* log of 64-1/2* log of 16	$\frac{1}{3} \cdot \log (64) - \frac{1}{2} \cdot \log (16)$
21870	Simplify/Condense	1/3* log of 64-1/2* log of 36	$\frac{1}{3} \cdot \log (64) - \frac{1}{2} \cdot \log (36)$
21871	Simplify/Condense	1/3* log of c^x+2 log of c^y-5 log of c^x	$\frac{1}{3} \cdot \log (c^{x}) + 2 \log (c^{y}) - 5 \log (c^{x})$
21872	Simplify/Condense	1/3* log of x^18-2 log of 3+4 log of x	$\frac{1}{3} \cdot \log (x^{18}) - 2 \log (3) + 4 \log (x)$
21873	Solve for x	(x^2-5)^(3/2)=64	${(x^{2} - 5)}^{\frac{3}{2}} = 64$
21874	Simplify/Condense	1/3( log of bx^4y^5)-3/4( log of bx^2y)	$\frac{1}{3} \cdot (\log (b) x^{4} y^{5}) - \frac{3}{4} \cdot (\log (b) x^{2} y)$
21875	Simplify/Condense	1/3* log of m+ log of n-4 log of p	$\frac{1}{3} \cdot \log (m) + \log (n) - 4 \log (p)$
21876	Simplify/Condense	1/3*( log of M-2 log of N)	$\frac{1}{3} \cdot (\log (M - 2) \log (N))$
21877	Simplify/Condense	1/3* log of x- log of y+4 log of z	$\frac{1}{3} \cdot \log (x) - \log (y) + 4 \log (z)$
21878	Simplify/Condense	1/4*(2 natural log of x+1+3 natural log of x-1- natural log of 6)	$\frac{1}{4} \cdot (2 \ln (x + 1) + 3 \ln (x - 1) - \ln (6))$
21879	Simplify/Condense	1/4*( log of 1.33)/( log of 1.025)	$\frac{1}{4} \cdot \frac{\log (1.33)}{\log (1.025)}$
21880	Simplify/Condense	1/4*( log base 9 of x+1+4 log base 9 of x-1)+12 log base 9 of x	$\frac{1}{4} \cdot (\log_{9} (x + 1) + 4 \log_{9} (x - 1)) + 12 \log_{9} (x)$
21881	Simplify/Condense	1/4* log of (x+3)^4+1/3*( log of x^6- log of (x^2-2x-15)^3)	$\frac{1}{4} \cdot \log ({(x + 3)}^{4}) + \frac{1}{3} \cdot (\log (x^{6}) - \log ({(x^{2} - 2 x - 15)}^{3}))$
21882	Simplify/Condense	1/4* log base 16 of 1/1048576	$\frac{1}{4} \cdot \log_{16} (\frac{1}{1048576})$
21883	Simplify/Condense	1/4* log base 3 of 5x	$\frac{1}{4} \cdot \log_{3} (5 x)$
21884	Simplify/Condense	1/4* log base 3 of x+3 log base 3 of 2x- log base 3 of 9	$\frac{1}{4} \cdot \log_{3} (x) + 3 \log_{3} (2 x) - \log_{3} (9)$
21885	Simplify/Condense	1/4* log base 3 of z+2 log base 3 of x- log base 3 of y	$\frac{1}{4} \cdot \log_{3} (z) + 2 \log_{3} (x) - \log_{3} (y)$
21886	Simplify/Condense	1/4* log base 4 of 16	$\frac{1}{4} \cdot \log_{4} (16)$
21887	Simplify/Condense	1/4* log base 5 of 81-(2 log base 5 of 6-1/2* log base 5 of 4)	$\frac{1}{4} \cdot \log_{5} (81) - (2 \log_{5} (6) - \frac{1}{2} \cdot \log_{5} (4))$
21888	Simplify/Condense	1/4* log base b of 16-2 log base b of 5+ log base b of 7	$\frac{1}{4} \cdot \log_{b} (16) - 2 \log_{b} (5) + \log_{b} (7)$
21889	Simplify/Condense	1/4* log base b of x+3 log base b of y-4 log base b of x	$\frac{1}{4} \cdot \log_{b} (x) + 3 \log_{b} (y) - 4 \log_{b} (x)$
21890	Simplify/Condense	1/4* log base b of x+4 log base b of y-5 log base b of x	$\frac{1}{4} \cdot \log_{b} (x) + 4 \log_{b} (y) - 5 \log_{b} (x)$
21891	Simplify/Condense	1/4*( log base b of x+5 log base b of y-2 log base b of x)	$\frac{1}{4} \cdot (\log_{b} (x + 5) \log_{b} (y - 2) \log_{b} (x))$
21892	Simplify/Condense	1/4* log base m of 7+7 log base m of x- log base m of z	$\frac{1}{4} \cdot \log_{m} (7) + 7 \log_{m} (x) - \log_{m} (z)$
21893	Simplify/Condense	1/4* natural log of 16-1/2* natural log of 64	$\frac{1}{4} \cdot \ln (16) - \frac{1}{2} \cdot \ln (64)$
21894	Simplify/Condense	1/4* natural log of 2-(14999 natural log of p)/8	$\frac{1}{4} \cdot \ln (2) - \frac{14999 \ln (p)}{8}$
21895	Simplify/Condense	-1/4* natural log of 9	$- \frac{1}{4} \cdot \ln (9)$
21896	Simplify/Condense	1/4*( natural log of ex)	$\frac{1}{4} \cdot (\ln (e) x)$
21897	Simplify/Condense	1/3* log of (x+2)^3+0.5( log of x^4- log of (x^2-x-6)^2)	$\frac{1}{3} \cdot \log ({(x + 2)}^{3}) + 0.5 (\log (x^{4}) - \log ({(x^{2} - x - 6)}^{2}))$
21898	Simplify/Condense	1/3* log of (x+2)^3	$\frac{1}{3} \cdot \log ({(x + 2)}^{3})$
21899	Solve for x	square root of 2 square root of 14x+8 = square root of 3x+4	$\sqrt{2 \sqrt{14 x + 8}} = \sqrt{3 x + 4}$
21900	Simplify/Condense	1/3* log of (x+2)^3+1/2*( log of x^4- log of (x^(2-2x-8))^2)	$\frac{1}{3} \cdot \log ({(x + 2)}^{3}) + \frac{1}{2} \cdot (\log (x^{4}) - \log ({(x^{2 - 2 x - 8})}^{2}))$