Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
22801	Simplify/Condense	4 log of 0.0001-3 natural log of fourth root of e	$4 \log (0.0001) - 3 \ln (\sqrt[4]{e})$
22802	Simplify/Condense	4 log of x^2+3 log of 2- log of 16	$4 \log (x^{2}) + 3 \log (2) - \log (16)$
22803	Simplify/Condense	4 log of x^2-3 log of x^2	$4 \log (x^{2}) - 3 \log (x^{2})$
22804	Simplify/Condense	4 log of x^2y^3+3* log of 1/x-6 log of y	$4 \log (x^{2} y^{3}) + 3 \cdot \log (\frac{1}{x}) - 6 \log (y)$
22805	Simplify/Condense	4 log of x^2y+3 log of 1/x-3 log of y	$4 \log (x^{2} y) + 3 \log (\frac{1}{x}) - 3 \log (y)$
22806	Simplify/Condense	4 log of x^3+3 log of 1/(x^5)	$4 \log (x^{3}) + 3 \log (\frac{1}{x^{5}})$
22807	Simplify/Condense	4 log of x-16 log of y	$4 \log (x) - 16 \log (y)$
22808	Simplify/Condense	4 log of x-2 log of y+ log of z	$4 \log (x) - 2 \log (y) + \log (z)$
22809	Simplify/Condense	4 log of x-5 log of x^6	$4 \log (x) - 5 \log (x^{6})$
22810	Simplify/Condense	4 log of x-6 log of y	$4 \log (x) - 6 \log (y)$
22811	Simplify/Condense	4 log of x- log of y	$4 \log (x) - \log (y)$
22812	Simplify/Condense	4 log of x-1/4 log of x^2+1+5 log of x-1	$4 \log (x - \frac{1}{4}) \log (x^{2} + 1) + 5 \log (x - 1)$
22813	Simplify/Condense	4 log of x+1-5 log of x+2 log of x-7	$4 \log (x + 1) - 5 \log (x) + 2 \log (x - 7)$
22814	Simplify/Condense	4 log of x+3-5 log of x^2+4+1/3* log of y	$4 \log (x + 3) - 5 \log (x^{2} + 4) + \frac{1}{3} \cdot \log (y)$
22815	Simplify/Condense	4 log of x-3=11	$4 \log (x - 3) = 11$
22816	Simplify/Condense	4 log of xy-2 log of x	$4 \log (x y) - 2 \log (x)$
22817	Simplify/Condense	4 log of y+2 log of x-1/2* log of z	$4 \log (y) + 2 \log (x) - \frac{1}{2} \cdot \log (z)$
22818	Simplify/Condense	4x natural log of 5+x natural log of 6+3 natural log of 6	$4 x \ln (5) + x \ln (6) + 3 \ln (6)$
22819	Simplify/Condense	4x natural log of e-7	$4 x \ln (e) - 7$
22820	Simplify/Condense	5(( log of 300)/( log of 2))	$5 (\frac{\log (300)}{\log (2)})$
22821	Simplify/Condense	(5( log base 2 of x))/6+(2( log base 2 of y))/3-( log base 2 of x)/2- log base 2 of y	$\frac{5 (\log_{2} (x))}{6} + \frac{2 (\log_{2} (y))}{3} - \frac{\log_{2} (x)}{2} - \log_{2} (y)$
22822	Simplify/Condense	-5e^( natural log of 3)	$- 5 e^{\ln (3)}$
22823	Simplify/Condense	5 log of x-2 log of x+6	$5 \log (x) - 2 \log (x + 6)$
22824	Simplify/Condense	5 log base 2 of cube root of 1/4	$5 \log_{2} (\sqrt[3]{\frac{1}{4}})$
22825	Simplify/Condense	5 log base 2 of x	$5 \log_{2} (x)$
22826	Simplify/Condense	5 log base 2 of x+10 log base 2 of y	$5 \log_{2} (x) + 10 \log_{2} (y)$
22827	Simplify/Condense	5 log base 2 of x+3 log base 2 of y	$5 \log_{2} (x) + 3 \log_{2} (y)$
22828	Simplify/Condense	5 log base 2 of y-7-3 log base 2 of y+8	$5 \log_{2} (y - 7) - 3 \log_{2} (y + 8)$
22829	Simplify/Condense	5 log base 3 of 2+1/5* log base 3 of r-2-1/2* log base 3 of r	$5 \log_{3} (2) + \frac{1}{5} \cdot \log_{3} (r - 2) - \frac{1}{2} \cdot \log_{3} (r)$
22830	Simplify/Condense	5 log base 3 of 27	$5 \log_{3} (27)$
22831	Simplify/Condense	5 log base 3 of x+ log base 3 of x-6	$5 \log_{3} (x) + \log_{3} (x - 6)$
22832	Simplify/Condense	5 log base 3 of x+7 log base 3 of y	$5 \log_{3} (x) + 7 \log_{3} (y)$
22833	Simplify/Condense	5 log base 3 of x-3 log base 3 of 9+1/2* log base 3 of y	$5 \log_{3} (x) - 3 \log_{3} (9) + \frac{1}{2} \cdot \log_{3} (y)$
22834	Simplify/Condense	5 log base 3 of x+2+2 log base 3 of 4x- log base 3 of 8x^5	$5 \log_{3} (x + 2) + 2 \log_{3} (4 x) - \log_{3} (8 x^{5})$
22835	Simplify/Condense	5 log base 4 of x^2-1-4 log base 4 of x+3	$5 \log_{4} (x^{2} - 1) - 4 \log_{4} (x + 3)$
22836	Simplify/Condense	5 log base 4 of 2+ log base 4 of 3	$5 \log_{4} (2) + \log_{4} (3)$
22837	Simplify/Condense	5 log base 4 of 2+7 log base 4 of x-4 log base 4 of y	$5 \log_{4} (2) + 7 \log_{4} (x - 4 \log_{4} (y))$
22838	Simplify/Condense	5 log base 4 of 3z+1+1/4* log base 4 of z+7	$5 \log_{4} (3 z + 1) + \frac{1}{4} \cdot \log_{4} (z + 7)$
22839	Simplify/Condense	20 log base 5 of 12+5 log base 5 of 7	$20 \log_{5} (12) + 5 \log_{5} (7)$
22840	Simplify/Condense	20 log base 8 of x+4 log base 8 of y	$20 \log_{8} (x) + 4 \log_{8} (y)$
22841	Simplify/Condense	20 natural log of 7-2 natural log of 12-3 natural log of x+5 natural log of y	$20 \ln (7) - 2 \ln (12) - 3 \ln (x) + 5 \ln (y)$
22842	Simplify/Condense	20 log of fifth root of x	$20 \log (\sqrt[5]{x})$
22843	Simplify/Condense	21 log base 3 of cube root of x+ log base 3 of 9x^2	$21 \log_{3} (\sqrt[3]{x}) + \log_{3} (9 x^{2})$
22844	Simplify/Condense	21 log base 3 of cube root of x+ log base 3 of 9x^2- log base 2 of 9	$21 \log_{3} (\sqrt[3]{x}) + \log_{3} (9 x^{2}) - \log_{2} (9)$
22845	Simplify/Condense	21 log base 3 of cube root of x+ log base 3 of 9x^2- log base 3 of 25	$21 \log_{3} (\sqrt[3]{x}) + \log_{3} (9 x^{2}) - \log_{3} (25)$
22846	Find the Range	y=1-sin(x)	$y = 1 - \sin (x)$
22847	Simplify/Condense	21 log base 3 of cube root of x+ log base 3 of 9x^2- log base 3 of 9	$21 \log_{3} (\sqrt[3]{x} + \log_{3} (9 x^{2}) - \log_{3} (9))$
22848	Simplify/Condense	21 natural log of x+ natural log of y-3 natural log of z	$21 \ln (x) + \ln (y) - 3 \ln (z)$
22849	Simplify/Condense	2-3 log base 4 of x	$2 - 3 \log_{4} (x)$
22850	Simplify/Condense	24110*( log of 50)/( log of 2)	$24110 \cdot \frac{\log (50)}{\log (2)}$
22851	Simplify/Condense	27( natural log of 1/(2/2000))^x	$27 {(\ln (\frac{1}{\frac{2}{2000}}))}^{x}$
22852	Simplify/Condense	2-8e^(-2 natural log of 2)	$2 - 8 e^{- 2 \ln (2)}$
22853	Simplify/Condense	280 natural log of 2350+1+1915	$280 \ln (2350 + 1) + 1915$
22854	Simplify/Condense	2 natural log of e^A+3 natural log of B^e	$2 \ln (e^{A}) + 3 \ln (B^{e})$
22855	Simplify/Condense	2 natural log of \|tan(x)\|	$2 \ln (\| \tan (x) \|)$
22856	Simplify/Condense	2 natural log of e^(2x+1)	$2 \ln (e^{2 x + 1})$
22857	Simplify/Condense	2 log base 9 of x+5 log base 9 of x-6	$2 \log_{9} (x) + 5 \log_{9} (x - 6)$
22858	Simplify/Condense	2 log base a of 5x^3-1/2* log base a of 2x+3	$2 \log_{a} (5 x^{3}) - \frac{1}{2} \cdot \log_{a} (2 x + 3)$
22859	Simplify/Condense	2 log base b of 2+ log base b of 5	$2 \log_{b} (2) + \log_{b} (5)$
22860	Simplify/Condense	2 log base b of 8- log base b of 2	$2 \log_{b} (8) - \log_{b} (2)$
22861	Simplify/Condense	2 log base b of q+7 log base b of x	$2 \log_{b} (q) + 7 \log_{b} (x)$
22862	Simplify/Condense	2 log base b of x- log base b of y	$2 \log_{b} (x) - \log_{b} (y)$
22863	Simplify/Condense	2 natural log of x^6+2 natural log of y^3-8 natural log of z^5	$2 \ln (x^{6}) + 2 \ln (y^{3}) - 8 \ln (z^{5})$
22864	Simplify/Condense	2 natural log of 2+3 natural log of z-4	$2 \ln (2) + 3 \ln (z - 4)$
22865	Simplify/Condense	2 natural log of 2+ natural log of x	$2 \ln (2) + \ln (x)$
22866	Simplify/Condense	2 natural log of 3+1/3* natural log of x+ natural log of (e)^y-1/2* natural log of z	$2 \ln (3) + \frac{1}{3} \cdot \ln (x) + \ln ({(e)}^{y}) - \frac{1}{2} \cdot \ln (z)$
22867	Simplify/Condense	2 natural log of 3x	$2 \ln (3 x)$
22868	Simplify/Condense	2 natural log of 3x+3=1	$2 \ln (3 x) + 3 = 1$
22869	Simplify/Condense	2- log base 2 of x-3	$2 - \log_{2} (x - 3)$
22870	Simplify/Condense	2 natural log of e^5	$2 \ln (e^{5})$
22871	Simplify/Condense	2 natural log of e^8- natural log of e^5	$2 \ln (e^{8}) - \ln (e^{5})$
22872	Simplify/Condense	2- natural log of 4	$2 - \ln (4)$
22873	Simplify/Condense	2 natural log of 4+4 natural log of 2	$2 \ln (4) + 4 \ln (2)$
22874	Simplify/Condense	2 natural log of 4+5 natural log of 3	$2 \ln (4) + 5 \ln (3)$
22875	Simplify/Condense	2 natural log of 4-4 natural log of x+0.5 natural log of y-4 natural log of z+6 natural log of w+3 natural log of t	$2 \ln (4) - 4 \ln (x) + 0.5 \ln (y) - 4 \ln (z) + 6 \ln (w) + 3 \ln (t)$
22876	Simplify/Condense	2 natural log of 5-1/2* natural log of 25	$2 \ln (5) - \frac{1}{2} \cdot \ln (25)$
22877	Simplify/Condense	2 natural log of 5+3 natural log of 4	$2 \ln (5) + 3 \ln (4)$
22878	Simplify/Condense	2 natural log of 5+4 natural log of x	$2 \ln (5) + 4 \ln (x)$
22879	Simplify/Condense	2 natural log of 5+5 natural log of z-8	$2 \ln (5) + 5 \ln (z - 8)$
22880	Simplify/Condense	2 natural log of 6+5 natural log of z-4	$2 \ln (6) + 5 \ln (z - 4)$
22881	Simplify/Condense	2 natural log of 6- natural log of 3	$2 \ln (6) - \ln (3)$
22882	Simplify/Condense	2 natural log of 8+5 natural log of z	$2 \ln (8) + 5 \ln (z)$
22883	Simplify/Condense	2 natural log of 8+7 natural log of z-4	$2 \ln (8) + 7 \ln (z - 4)$
22884	Simplify/Condense	2 natural log of 8+9 natural log of z-4	$2 \ln (8) + 9 \ln (z - 4)$
22885	Simplify/Condense	2 natural log of 8-2 natural log of 4	$2 \ln (8) - 2 \ln (4)$
22886	Simplify/Condense	2 natural log of 8+2 natural log of y	$2 \ln (8 + 2) \ln (y)$
22887	Simplify/Condense	2 natural log of a+1/2* natural log of b-3 natural log of c	$2 \ln (a) + \frac{1}{2} \cdot \ln (b) - 3 \ln (c)$
22888	Simplify/Condense	2 natural log of a+5 natural log of z-4	$2 \ln (a) + 5 \ln (z - 4)$
22889	Simplify/Condense	2 natural log of a-3 natural log of b+1/2* natural log of c	$2 \ln (a) - 3 \ln (b) + \frac{1}{2} \cdot \ln (c)$
22890	Simplify/Condense	2 log base b of x+9 log base b of z	$2 \log_{b} (x) + 9 \log_{b} (z)$
22891	Simplify/Condense	2 log base b of z+1+ log base b of 3z+5	$2 \log_{b} (z + 1) + \log_{b} (3 z + 5)$
22892	Simplify/Condense	2 log base c of m-5/3* log base c of n+1/4* log base c of j-5 log base c of k	$2 \log_{c} (m) - \frac{5}{3} \cdot \log_{c} (n) + \frac{1}{4} \cdot \log_{c} (j) - 5 \log_{c} (k)$
22893	Simplify/Condense	2 log base p of r+1/2* log base p of z-3/2* log base p of y-2 log base p of a	$2 \log_{p} (r) + \frac{1}{2} \cdot \log_{p} (z) - \frac{3}{2} \cdot \log_{p} (y) - 2 \log_{p} (a)$
22894	Simplify/Condense	2 log base x of 3+ log base x of 3	$2 \log_{x} (3) + \log_{x} (3)$
22895	Simplify/Condense	2 log base 5 of x+1- log base 5 of x+1+ log base 5 of x^2	$2 \log_{5} (x + 1) - \log_{5} (x + 1) + \log_{5} (x^{2})$
22896	Simplify/Condense	2 log base 5 of y-3 log base 5 of 4+1/2* log base 5 of z	$2 \log_{5} (y) - 3 \log_{5} (4) + \frac{1}{2} \cdot \log_{5} (z)$
22897	Simplify/Condense	2 log base 6 of x/3-4 log base 6 of 1/y	$2 \log_{6} (\frac{x}{3}) - 4 \log_{6} (\frac{1}{y})$
22898	Simplify/Condense	2 log base 6 of 12+ log base 6 of 4	$2 \log_{6} (12) + \log_{6} (4)$
22899	Simplify/Condense	2 log base 6 of 2+1/7* log base 6 of r-4-1/2* log base 6 of r	$2 \log_{6} (2) + \frac{1}{7} \cdot \log_{6} (r - 4) - \frac{1}{2} \cdot \log_{6} (r)$
22900	Simplify/Condense	2 log base 6 of 3+1/4* log base 6 of r-8-1/2* log base 6 of r	$2 \log_{6} (3) + \frac{1}{4} \cdot \log_{6} (r - 8) - \frac{1}{2} \cdot \log_{6} (r)$