Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
17501	Simplify/Condense	2(3 natural log of x- natural log of x+1- natural log of x-1)	$2 (3 \ln (x) - \ln (x + 1) - \ln (x - 1))$
17502	Simplify/Condense	12 log of 12(24)	$12 \log (12) (24)$
17503	Simplify/Condense	2 log base 2 of x+4 log base 2 of y	$2 \log_{2} (x) + 4 \log_{2} (y)$
17504	Simplify/Condense	2 log base 2 of 12- log base 2 of 4+ log base 2 of 3	$2 \log_{2} (12) - \log_{2} (4) + \log_{2} (3)$
17505	Simplify/Condense	2 log base 7 of 5+ log base 7 of x+1- log base 7 of x^2-4	$2 \log_{7} (5) + \log_{7} (x + 1) - \log_{7} (x^{2} - 4)$
17506	Simplify/Condense	-2 natural log of 4	$- 2 \ln (4)$
17507	Simplify/Condense	2 natural log of e^3-6 natural log of x+4	$2 \ln (e^{3}) - 6 \ln (x + 4)$
17508	Simplify/Condense	2 natural log of cube root of e	$2 \ln (\sqrt[3]{e})$
17509	Simplify/Condense	-2 log base 9 of 5	$- 2 \log_{9} (5)$
17510	Simplify/Condense	3 log of x	$3 \log (x)$
17511	Simplify/Condense	3 log of x-1/5* log of x^2+1+2 log of x-1	$3 \log (x) - \frac{1}{5} \cdot \log (x^{2} + 1) + 2 \log (x - 1)$
17512	Simplify/Condense	3 log of x+ log of 3-3 log of y	$3 \log (x) + \log (3) - 3 \log (y)$
17513	Simplify/Condense	4 natural log of 2+0.5 natural log of 9- natural log of 6	$4 \ln (2) + 0.5 \ln (9) - \ln (6)$
17514	Simplify/Condense	3 natural log of x+4 natural log of y	$3 \ln (x) + 4 \ln (y)$
17515	Simplify/Condense	3 natural log of x-2-4 natural log of x	$3 \ln (x - 2) - 4 \ln (x)$
17516	Simplify/Condense	3 log of 2x+ log of x^2-1-2 log of x+1-2 log of 8	$3 \log (2 x) + \log (x^{2} - 1) - 2 \log (x + 1) - 2 \log (8)$
17517	Simplify/Condense	5 natural log of x+8-2 natural log of x	$5 \ln (x + 8) - 2 \ln (x)$
17518	Simplify/Condense	6 log base 4 of x-1/4 log base 4 of z+41 log base 4 of y	$6 \log_{4} (x - \frac{1}{4}) \log_{4} (z + 41) \log_{4} (y)$
17519	Simplify/Condense	62+35 log of 14-4	$62 + 35 \log (14 - 4)$
17520	Simplify/Condense	6 natural log of x-4+1/6* natural log of (x)^36-12 natural log of (x+2)^9	$6 \ln (x - 4) + \frac{1}{6} \cdot \ln ({(x)}^{36}) - 12 \ln ({(x + 2)}^{9})$
17521	Simplify/Condense	-6 natural log of x-7 natural log of y+1/7 natural log of z	$- 6 \ln (x - 7) \ln (y + \frac{1}{7}) \ln (z)$
17522	Simplify/Condense	7 log base b of x+8 log base b of z	$7 \log_{b} (x) + 8 \log_{b} (z)$
17523	Simplify/Condense	7 log base 2 of 7*x+67	$7 \log_{2} (7 \cdot x + 67)$
17524	Simplify/Condense	8 log base 3 of 12+2 log base 3 of 5	$8 \log_{3} (12) + 2 \log_{3} (5)$
17525	Simplify/Condense	5 log base b of q+2 log base b of y	$5 \log_{b} (q) + 2 \log_{b} (y)$
17526	Simplify/Condense	5 log base 4 of a-6 log base 4 of b	$5 \log_{4} (a) - 6 \log_{4} (b)$
17527	Simplify/Condense	log of ( cube root of xz^2)/( square root of y)	$\log (\frac{\sqrt[3]{x z^{2}}}{\sqrt{y}})$
17528	Simplify/Condense	natural log of x+ natural log of 1-x	$\ln (x) + \ln (1 - x)$
17529	Solve for ?	cot(theta) = square root of 3	$\cot (θ) = \sqrt{3}$
17530	Simplify/Condense	natural log of (e^3 fourth root of x^2)/( cube root of y)	$\ln (\frac{e^{3} \sqrt[4]{x^{2}}}{\sqrt[3]{y}})$
17531	Simplify/Condense	6 natural log of x+5-7 natural log of x	$6 \ln (x + 5) - 7 \ln (x)$
17532	Solve for ?	4sin(theta)^2=3	$4 \sin^{2} (θ) = 3$
17533	Simplify/Condense	natural log of 3-2( natural log of 4+ natural log of 32)	$\ln (3) - 2 (\ln (4) + \ln (32))$
17534	Simplify/Condense	natural log of 5+ natural log of 7+2 natural log of 6	$\ln (5) + \ln (7) + 2 \ln (6)$
17535	Simplify/Condense	natural log of 5x square root of 3x-1	$\ln (5 x \sqrt{3 x - 1})$
17536	Simplify	((rs^2)^3)/((r^-3s^2)^2)	$\frac{{(r s^{2})}^{3}}{{(r^{- 3} s^{2})}^{2}}$
17537	Simplify/Condense	natural log of x/(x-2)+ natural log of (x+2)/x- natural log of x^2-4	$\ln (\frac{x}{x - 2}) + \ln (\frac{x + 2}{x}) - \ln (x^{2} - 4)$
17538	Simplify/Condense	natural log of 3+1/2* natural log of x+ natural log of y-1/3* natural log of z	$\ln (3) + \frac{1}{2} \cdot \ln (x) + \ln (y) - \frac{1}{3} \cdot \ln (z)$
17539	Simplify/Condense	natural log of 35x^954	$\ln (35 x^{954})$
17540	Simplify/Condense	natural log of e^4y+ natural log of ey-5	$\ln (e^{4} y) + \ln (e y) - 5$
17541	Solve for y	square root of y+2<=3	$\sqrt{y + 2} \leq 3$
17542	Find the Vertices	4x^2+25y^2=100	$4 x^{2} + 25 y^{2} = 100$
17543	Simplify/Condense	natural log of x^6-2 natural log of square root of x^5	$\ln (x^{6}) - 2 \ln (\sqrt{x^{5}})$
17544	Simplify/Condense	log of x- log of x+3	$\log (x) - \log (x + 3)$
17545	Simplify/Condense	( natural log of 30- natural log of 3)/( natural log of 100- natural log of 1)+ natural log of 9-1/2- natural log of 10* log of 9	$\frac{\ln (30) - \ln (3)}{\ln (100) - \ln (1)} + \ln (9) - \frac{1}{2} - \ln (10) \cdot \log (9)$
17546	Simplify/Condense	1/2* log of b+5 log of c	$\frac{1}{2} \cdot \log (b) + 5 \log (c)$
17547	Simplify/Condense	natural log of 7-3 natural log of x	$\ln (7) - 3 \ln (x)$
17548	Simplify/Condense	1/2*( natural log of x+1+2 natural log of x-1)+3 natural log of x	$\frac{1}{2} \cdot (\ln (x + 1) + 2 \ln (x - 1)) + 3 \ln (x)$
17549	Simplify/Condense	1/2* log of x-1/4* log of y+1/3* log of z	$\frac{1}{2} \cdot \log (x) - \frac{1}{4} \cdot \log (y) + \frac{1}{3} \cdot \log (z)$
17550	Simplify/Condense	1/2* log base y of p^3q^4-2/3* log base y of p^4q^3	$\frac{1}{2} \cdot \log_{y} (p^{3} q^{4}) - \frac{2}{3} \cdot \log_{y} (p^{4} q^{3})$
17551	Simplify/Condense	1/2* natural log of 2x-1-2 natural log of x+1	$\frac{1}{2} \cdot \ln (2 x - 1) - 2 \ln (x + 1)$
17552	Simplify/Condense	1/2*( log base 4 of x+1+2 log base 4 of x-1)+6 log base 4 of x	$\frac{1}{2} \cdot (\log_{4} (x + 1) + 2 \log_{4} (x - 1)) + 6 \log_{4} (x)$
17553	Simplify/Condense	1/3*( log base 8 of y+2 log base 8 of y+4)- log base 8 of y-1	$\frac{1}{3} \cdot (\log_{8} (y) + 2 \log_{8} (y + 4)) - \log_{8} (y - 1)$
17554	Simplify/Condense	1/2* log of x- log of y-2 log of z	$\frac{1}{2} \cdot \log (x) - \log (y) - 2 \log (z)$
17555	Simplify/Condense	1/(2 natural log of 2)-1/(3 natural log of 3)+1/(4 natural log of 4)-1/(5 natural log of 5)	$\frac{1}{2 \ln (2)} - \frac{1}{3 \ln (3)} + \frac{1}{4 \ln (4)} - \frac{1}{5 \ln (5)}$
17556	Simplify/Condense	1/5*( log base 4 of x+ log base 4 of 7)-( log base 4 of y)	$\frac{1}{5} \cdot (\log_{4} (x) + \log_{4} (7)) - (\log_{4} (y))$
17557	Simplify/Condense	1/4* log of x^2-2 log of y+ log of 4	$\frac{1}{4} \cdot \log (x^{2}) - 2 \log (y) + \log (4)$
17558	Simplify/Condense	10^( log of 3)	$10^{\log (3)}$
17559	Simplify/Condense	1/7* natural log of x	$\frac{1}{7} \cdot \ln (x)$
17560	Simplify/Condense	10^( log of z)	$10^{\log (z)}$
17561	Simplify/Condense	2/3* log base 7 of z-2	$\frac{2}{3} \cdot \log_{7} (z - 2)$
17562	Simplify/Condense	3/2* log base 2 of x+y+ log of x-y- log base 2 of x^2-y^2	$\frac{3}{2} \cdot \log_{2} (x + y) + \log (x - y) - \log_{2} (x^{2} - y^{2})$
17563	Simplify/Condense	5^( log base 25 of 3)	$5^{\log_{25} (3)}$
17564	Simplify/Condense	10^( log of 6)	$10^{\log (6)}$
17565	Simplify/Condense	5/2* log base 7 of z-4	$\frac{5}{2} \cdot \log_{7} (z - 4)$
17566	Simplify/Condense	5^( log base 5 of 17)	$5^{\log_{5} (17)}$
17567	Simplify/Condense	9^( log base 9 of 15)	$9^{\log_{9} (15)}$
17568	Simplify/Condense	9^( log of 9(7))	$9^{\log (9 (7))}$
17569	Simplify/Condense	3/5* log base a of x^15y^10+12 log base a of x^(3/4)-13 log base a of y	$\frac{3}{5} \cdot \log_{a} (x^{15} y^{10}) + 12 \log_{a} (x^{\frac{3}{4}}) - 13 \log_{a} (y)$
17570	Simplify/Condense	5^(2 log base 5 of 6)	$5^{2 \log_{5} (6)}$
17571	Simplify/Condense	( log of 20+2 log of 7- log of 5)/( log of 14)	$\frac{\log (20) + 2 \log (7) - \log (5)}{\log (14)}$
17572	Simplify/Condense	e^(-3 log of natural log of t)	$e^{- 3 \log (\ln (t))}$
17573	Simplify/Condense	e^( natural log of square root of 2)	$e^{\ln (\sqrt{2})}$
17574	Simplify/Condense	e^( natural log of 4)	$e^{\ln (4)}$
17575	Simplify/Condense	e^( natural log of 4x^2)	$e^{\ln (4 x^{2})}$
17576	Simplify/Condense	e^( natural log of natural log of x)	$e^{\ln (\ln (x))}$
17577	Simplify/Condense	e^( natural log of 5)	$e^{\ln (5)}$
17578	Simplify/Condense	e^( natural log of 5x)	$e^{\ln (5 x)}$
17579	Simplify/Condense	log base 11 of 11^7	$\log_{11} (11^{7})$
17580	Simplify/Condense	log base 15 of 5+ log base 15 of 3	$\log_{15} (5) + \log_{15} (3)$
17581	Simplify/Condense	log base 14 of 2+ log base 14 of 7	$\log_{14} (2) + \log_{14} (7)$
17582	Simplify/Condense	log base 12 of 4+ log base 12 of 36	$\log_{12} (4) + \log_{12} (36)$
17583	Simplify/Condense	log base 16 of 2+ log base 16 of 8	$\log_{16} (2) + \log_{16} (8)$
17584	Simplify/Condense	log base 18 of 6+ log base 18 of 3	$\log_{18} (6) + \log_{18} (3)$
17585	Simplify/Condense	log of 400+ log of 5/2	$\log (400) + \log (\frac{5}{2})$
17586	Simplify/Condense	log of x^2-9- log of x^2+7x+12	$\log (x^{2} - 9) - \log (x^{2} + 7 x + 12)$
17587	Simplify/Condense	natural log of (e)^(-t)	$\ln ({(e)}^{- t})$
17588	Simplify/Condense	( log of 2)/( log of 16)	$\frac{\log (2)}{\log (16)}$
17589	Simplify/Condense	log base 2 of 1024	$\log_{2} (1024)$
17590	Simplify/Condense	log base 2 of x^7	$\log_{2} (x^{7})$
17591	Simplify/Condense	log base 2 of 0.04+2 log base 2 of 5	$\log_{2} (0.04) + 2 \log_{2} (5)$
17592	Simplify/Condense	log base 2 of 4^2*3^4	$\log_{2} (4^{2} \cdot 3^{4})$
17593	Simplify/Condense	log base 16 of 64+ log base 16 of 4	$\log_{16} (64) + \log_{16} (4)$
17594	Simplify/Condense	log base 2 of 1/128	$\log_{2} (\frac{1}{128})$
17595	Simplify/Condense	log base 2 of square root of 8	$\log_{2} (\sqrt{8})$
17596	Simplify/Condense	log base 2 of 6+3 log base 2 of 3-2 log base 2 of 5- log base 2 of 7	$\log_{2} (6) + 3 \log_{2} (3) - 2 \log_{2} (5) - \log_{2} (7)$
17597	Simplify/Condense	log base 3 of 243-2 log base 3 of 3	$\log_{3} (243) - 2 \log_{3} (3)$
17598	Simplify/Condense	log base 3 of 13+ log base 3 of y	$\log_{3} (13) + \log_{3} (y)$
17599	Simplify/Condense	log base 3 of 15- log base 3 of 30+ log base 3 of 54	$\log_{3} (15) - \log_{3} (30) + \log_{3} (54)$
17600	Simplify/Condense	log base 3 of 6^3+ log base 3 of 9^6	$\log_{3} (6^{3}) + \log_{3} (9^{6})$