Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
22501	Simplify/Condense	5 natural log of 2+5 natural log of x+3 natural log of y	$5 \ln (2) + 5 \ln (x) + 3 \ln (y)$
22502	Simplify/Condense	5 natural log of 4+3 natural log of 2	$5 \ln (4) + 3 \ln (2)$
22503	Simplify/Condense	5 natural log of 4-3 natural log of 5	$5 \ln (4) - 3 \ln (5)$
22504	Simplify/Condense	5 log base b of q- log base b of r	$5 \log_{b} (q - \log_{b} (r))$
22505	Simplify/Condense	4 log of 3A+4 log of 3B-5 log of 3C	$4 \log (3) A + 4 \log (3) B - 5 \log (3) C$
22506	Simplify/Condense	4 log of 4(5x)	$4 \log (4 (5 x))$
22507	Simplify/Condense	4 log of 5z+( log of 5x)/2	$4 \log (5) z + \frac{\log (5) x}{2}$
22508	Simplify/Condense	4 log of x-1/5* log of x^2+1+2 log of x-1	$4 \log (x) - \frac{1}{5} \cdot \log (x^{2} + 1) + 2 \log (x - 1)$
22509	Simplify/Condense	4 log of x+2 log of x-4	$4 \log (x) + 2 \log (x - 4)$
22510	Simplify/Condense	4 log of x+2 log of y	$4 \log (x) + 2 \log (y)$
22511	Simplify/Condense	4 log of x+3 log of y	$4 \log (x) + 3 \log (y)$
22512	Simplify/Condense	4 log of x+3 log of y-2 log of z	$4 \log (x) + 3 \log (y) - 2 \log (z)$
22513	Simplify/Condense	4 log of x+5 log of y-2 log of z	$4 \log (x) + 5 \log (y) - 2 \log (z)$
22514	Simplify/Condense	4 log of x+6 log of x-5	$4 \log (x) + 6 \log (x - 5)$
22515	Simplify/Condense	4 log of x+7 log of y-8 log of z	$4 \log (x) + 7 \log (y) - 8 \log (z)$
22516	Simplify/Condense	5 log of x+ log of 3-(3 log of 3+5 log of y)	$5 \log (x) + \log (3) - (3 \log (3) + 5 \log (y))$
22517	Simplify/Condense	5 log of x-2 log of x-6	$5 \log (x) - 2 \log (x - 6)$
22518	Simplify/Condense	5 log of x-2 log of y+4 log of z	$5 \log (x) - 2 \log (y) + 4 \log (z)$
22519	Simplify/Condense	5 log of x-3 log of x-3	$5 \log (x) - 3 \log (x - 3)$
22520	Simplify/Condense	5 log of x-4 log of x^2+1+3 log of x-1	$5 \log (x) - 4 \log (x^{2} + 1 + 3 \log (x - 1))$
22521	Simplify/Condense	5 log of x-5 log of x^2+1+3 log of x-1	$5 \log (x) - 5 \log (x^{2} + 1) + 3 \log (x - 1)$
22522	Convert to Rectangular Coordinates	(-4,pi/3)	$(- 4, \frac{π}{3})$
22523	Simplify/Condense	5 log of x-7 log of y^6	$5 \log (x) - 7 \log (y^{6})$
22524	Simplify/Condense	5 log of z- log of y-3 log of x	$5 \log (z) - \log (y) - 3 \log (x)$
22525	Simplify/Condense	6* log of 10	$6 \cdot \log (10)$
22526	Simplify/Condense	6(2 natural log of x- natural log of x+4- natural log of x-4)	$6 (2 \ln (x) - \ln (x + 4) - \ln (x - 4))$
22527	Simplify/Condense	6( natural log of z+ natural log of z+7)-3 natural log of z-7	$6 (\ln (z) + \ln (z + 7)) - 3 \ln (z - 7)$
22528	Simplify/Condense	6e^(-4 natural log of x)	$6 e^{- 4 \ln (x)}$
22529	Simplify/Condense	6 log of 7-7 log of 6	$6 \log (7) - 7 \log (6)$
22530	Simplify/Condense	6 log of x+5 log of x-7	$6 \log (x) + 5 \log (x - 7)$
22531	Simplify/Condense	6 log base 2 of 2/3+2 log base 2 of 1/6-4 log base 2 of 2/9	$6 \log_{2} (\frac{2}{3}) + 2 \log_{2} (\frac{1}{6}) - 4 \log_{2} (\frac{2}{9})$
22532	Simplify/Condense	6 log base 2 of a-5 log base 2 of b-3 log base 2 of c	$6 \log_{2} (a) - 5 \log_{2} (b) - 3 \log_{2} (c)$
22533	Simplify/Condense	6 log base 2 of u-24 log base 2 of v	$6 \log_{2} (u) - 24 \log_{2} (v)$
22534	Simplify/Condense	6 log base 2 of x+7 log base 2 of y-4 log base 2 of z	$6 \log_{2} (x) + 7 \log_{2} (y) - 4 \log_{2} (z)$
22535	Simplify/Condense	6 log base 3 of 2-4 log base 3 of x	$6 \log_{3} (2) - 4 \log_{3} (x)$
22536	Simplify/Condense	6 log base 3 of 8-4 log base 3 of 7	$6 \log_{3} (8) - 4 \log_{3} (7)$
22537	Simplify/Condense	6 log base 3 of a+6 log base 3 of b	$6 \log_{3} (a) + 6 \log_{3} (b)$
22538	Simplify/Condense	6 log base 3 of x+6 log base 3 of u	$6 \log_{3} (x) + 6 \log_{3} (u)$
22539	Simplify/Condense	5 natural log of x-9 natural log of x	$5 \ln (x) - 9 \ln (x)$
22540	Simplify/Condense	5 natural log of x+4-9 natural log of x	$5 \ln (x + 4) - 9 \ln (x)$
22541	Simplify/Condense	5 natural log of x+5-4 natural log of x	$5 \ln (x + 5) - 4 \ln (x)$
22542	Factor	2x^3-4x^2-10x+20	$2 x^{3} - 4 x^{2} - 10 x + 20$
22543	Simplify/Condense	5 natural log of x-1/3* natural log of y	$5 \ln (x) - \frac{1}{3} \cdot \ln (y)$
22544	Simplify/Condense	5 natural log of x-1/5* natural log of y	$5 \ln (x) - \frac{1}{5} \cdot \ln (y)$
22545	Simplify/Condense	5 natural log of x+2 natural log of y-3 natural log of z	$5 \ln (x) + 2 \ln (y) - 3 \ln (z)$
22546	Simplify/Condense	5 natural log of x+4 natural log of y-3 natural log of z	$5 \ln (x) + 4 \ln (y - 3) \ln (z)$
22547	Simplify/Condense	5 natural log of x-3 natural log of y	$5 \ln (x - 3) \ln (y)$
22548	Simplify/Condense	5 log of 13x	$5 \log (13 x)$
22549	Simplify/Condense	5 log of 2-3 log of 2+1	$5 \log (2) - 3 \log (2 + 1)$
22550	Simplify/Condense	5 log of p-2/4* log of q	$5 \log (p) - \frac{2}{4} \cdot \log (q)$
22551	Simplify/Condense	5 log of w+7 log of x+4 log of y	$5 \log (w) + 7 \log (x) + 4 \log (y)$
22552	Simplify/Condense	5 log of x-1/4* log of x^2+1+5 log of x-1	$5 \log (x) - \frac{1}{4} \cdot \log (x^{2} + 1) + 5 \log (x - 1)$
22553	Simplify/Condense	5 log of x-1/5* log of x^2+1+2 log of x-1	$5 \log (x) - \frac{1}{5} \cdot \log (x^{2} + 1) + 2 \log (x - 1)$
22554	Find the Vertices	49x^2-16y^2=784	$49 x^{2} - 16 y^{2} = 784$
22555	Simplify/Condense	8 log base 5 of square root of 7x-2- log base 5 of 5/x+ log base 5 of 5	$8 \log_{5} (\sqrt{7 x - 2}) - \log_{5} (\frac{5}{x}) + \log_{5} (5)$
22556	Simplify/Condense	8 log base 5 of p+9 log base 5 of q-2 log base 5 of t	$8 \log_{5} (p) + 9 \log_{5} (q) - 2 \log_{5} (t)$
22557	Simplify/Condense	8 log base 6 of square root of 4x^-1- log base 6 of 7/x+ log base 6 of 7	$8 \log_{6} (\sqrt{4 x^{- 1}}) - \log_{6} (\frac{7}{x}) + \log_{6} (7)$
22558	Simplify/Condense	8 log base 6 of square root of 5x-7- log base 6 of 5/x+ log base 6 of 5	$8 \log_{6} (\sqrt{5 x - 7}) - \log_{6} (\frac{5}{x}) + \log_{6} (5)$
22559	Simplify/Condense	8 log base 6 of u+2 log base 6 of v	$8 \log_{6} (u) + 2 \log_{6} (v)$
22560	Simplify/Condense	8 log base 6 of x+(3 log base 6 of y(-1))/2* log base 6 of z	$8 \log_{6} (x) + \frac{3 \log_{6} (y) (- 1)}{2} \cdot \log_{6} (z)$
22561	Simplify/Condense	8 log base 8 of x+4 log base 8 of z	$8 \log_{8} (x + 4) \log_{8} (z)$
22562	Simplify/Condense	8 log base a of 0.25m+12 log base a of 0.25n-3 log base a of 0.25a+5 log base a of 0.25b	$8 \log_{a} (0.25 m) + 12 \log_{a} (0.25 n) - 3 \log_{a} (0.25 a) + 5 \log_{a} (0.25 b)$
22563	Simplify/Condense	8 log base b of x+3 log base b of z	$8 \log_{b} (x) + 3 \log_{b} (z)$
22564	Simplify/Condense	8 log base b of x+4 log base b of z	$8 \log_{b} (x) + 4 \log_{b} (z)$
22565	Simplify/Condense	8 log base b of x-9( log base b of y+ log base b of z)	$8 \log_{b} (x) - 9 (\log_{b} (y) + \log_{b} (z))$
22566	Simplify/Condense	7 log base 2 of u+3 log base 2 of v	$7 \log_{2} (u) + 3 \log_{2} (v)$
22567	Simplify/Condense	7 log base 7 of x-1/4* log base 7 of w	$7 \log_{7} (x) - \frac{1}{4} \cdot \log_{7} (w)$
22568	Simplify/Condense	7 log base 7 of z-1/2* log base 7 of w+5 log base 7 of y	$7 \log_{7} (z) - \frac{1}{2} \cdot \log_{7} (w) + 5 \log_{7} (y)$
22569	Simplify/Condense	7 log base b of x+6 log base b of x	$7 \log_{b} (x) + 6 \log_{b} (x)$
22570	Simplify/Condense	7 log of w-1/4* log of z+4 log of y	$7 \log (w) - \frac{1}{4} \cdot \log (z) + 4 \log (y)$
22571	Simplify/Condense	7 log base b of y+2 log base b of z	$7 \log_{b} (y) + 2 \log_{b} (z)$
22572	Simplify/Condense	70000e^((( natural log of 2)/25)*60)	$70000 e^{(\frac{\ln (2)}{25}) \cdot 60}$
22573	Simplify/Condense	72+253e^(1/10* natural log of 128/253*30)	$72 + 253 e^{\frac{1}{10} \cdot \ln (\frac{128}{253}) \cdot 30}$
22574	Simplify/Condense	75-6 natural log of 2+1	$75 - 6 \ln (2 + 1)$
22575	Simplify/Condense	79+106e^((45/30) natural log of 79/106)	$79 + 106 e^{(\frac{45}{30}) \ln (\frac{79}{106})}$
22576	Simplify/Condense	79+106e^(127/30* natural log of 71/106)	$79 + 106 e^{\frac{127}{30} \cdot \ln (\frac{71}{106})}$
22577	Simplify/Condense	7 natural log of 5 natural log of 5	$7 \ln (5) \ln (5)$
22578	Simplify/Condense	7 natural log of x-1/3* natural log of x^2+1	$7 \ln (x) - \frac{1}{3} \cdot \ln (x^{2} + 1)$
22579	Simplify/Condense	7 natural log of x-1/8* natural log of y	$7 \ln (x) - \frac{1}{8} \cdot \ln (y)$
22580	Simplify/Condense	7 natural log of x+8 natural log of y-4 natural log of z	$7 \ln (x) + 8 \ln (y) - 4 \ln (z)$
22581	Simplify/Condense	7 natural log of x+ natural log of x+1	$7 \ln (x) + \ln (x + 1)$
22582	Simplify/Condense	7 natural log of x-3 natural log of y	$7 \ln (x) - 3 \ln (y)$
22583	Simplify/Condense	7 natural log of x+3-2 natural log of x	$7 \ln (x + 3) - 2 \ln (x)$
22584	Simplify/Condense	7 natural log of x+3-6 natural log of x	$7 \ln (x + 3) - 6 \ln (x)$
22585	Simplify/Condense	7 natural log of x+5-5 natural log of x	$7 \ln (x + 5) - 5 \ln (x)$
22586	Simplify/Condense	7 natural log of x+5-8 natural log of x	$7 \ln (x + 5) - 8 \ln (x)$
22587	Simplify/Condense	7 natural log of x+6-7 natural log of x	$7 \ln (x + 6) - 7 \ln (x)$
22588	Simplify/Condense	7 natural log of x+6-9 natural log of x	$7 \ln (x + 6) - 9 \ln (x)$
22589	Simplify/Condense	7 natural log of x-3-7 natural log of x	$7 \ln (x - 3) - 7 \ln (x)$
22590	Simplify/Condense	7 natural log of xy-2 natural log of yz	$7 \ln (x y) - 2 \ln (y z)$
22591	Simplify/Condense	7 natural log of xy-5 natural log of 9yz	$7 \ln (x y) - 5 \ln (9 y z)$
22592	Simplify/Condense	7 log of 9	$7 \log (9)$
22593	Simplify/Condense	7 log of x+2 log of x- log of x	$7 \log (x) + 2 \log (x) - \log (x)$
22594	Simplify/Condense	7 log of x-11 log of y	$7 \log (x) - 11 \log (y)$
22595	Simplify/Condense	8* log of 10	$8 \cdot \log (10)$
22596	Simplify/Condense	8( natural log of z+ natural log of z+3)-9 natural log of z-1	$8 (\ln (z) + \ln (z + 3)) - 9 \ln (z - 1)$
22597	Simplify/Condense	6 log of square root of x+ log of 5-2 log of x	$6 \log (\sqrt{x}) + \log (5) - 2 \log (x)$
22598	Simplify/Condense	6 log of 11 square root of 11	$6 \log (11) \sqrt{11}$
22599	Simplify/Condense	6 log of 3y-2 log of x+5 log of z	$6 \log (3 y) - 2 \log (x) + 5 \log (z)$
22600	Simplify/Condense	6 log of 9x-24 log of 9y	$6 \log (9) x - 24 \log (9) y$