Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
32501	Evaluate	3^(4 log base 3 of 2)	$3^{4 \log_{3} (2)}$
32502	Evaluate	3^(4 log base 3 of 4)	$3^{4 \log_{3} (4)}$
32503	Evaluate	3^(5 log base 3 of 2+2)	$3^{5 \log_{3} (2 + 2)}$
32504	Evaluate	1/2* log of 3	$\frac{1}{2} \cdot \log (3)$
32505	Evaluate	1/2*( log of 6x)+ log of 6y	$\frac{1}{2} \cdot (\log (6) x) + \log (6) y$
32506	Evaluate	1/2* log of 81- log of 3	$\frac{1}{2} \cdot \log (81) - \log (3)$
32507	Evaluate	1/2* log of a+7 log of b	$\frac{1}{2} \cdot \log (a) + 7 \log (b)$
32508	Evaluate	1/2* log of n+3 log of m	$\frac{1}{2} \cdot \log (n) + 3 \log (m)$
32509	Evaluate	1/2* log of x-5	$\frac{1}{2} \cdot \log (x - 5)$
32510	Evaluate	1/20* natural log of 170/180	$\frac{1}{20} \cdot \ln (\frac{170}{180})$
32511	Evaluate	-1/(2 natural log of 2)	$- \frac{1}{2 \ln (2)}$
32512	Evaluate	1/3(5- log of 526)	$\frac{1}{3} \cdot (5 - \log (5) \cdot 26)$
32513	Evaluate	log base 9 of (5)^-4	$\log_{9} ({(5)}^{- 4})$
32514	Evaluate	log base 9 of (9)^11	$\log_{9} ({(9)}^{11})$
32515	Evaluate	log base 9 of (9)^13	$\log_{9} ({(9)}^{13})$
32516	Evaluate	log base 9 of (9)^3	$\log_{9} ({(9)}^{3})$
32517	Evaluate	log base a of (30a)^3	$\log_{a} ({(30 a)}^{3})$
32518	Evaluate	log base a of (8)^79	$\log_{a} ({(8)}^{79})$
32519	Evaluate	log base b of ( square root of (x^9)/(y^7z^9))^(1/7)	$\log_{b} ({(\sqrt{\frac{x^{9}}{y^{7} z^{9}}})}^{\frac{1}{7}})$
32520	Evaluate	( log base b of a* log base a of b)/( log of 10)	$\frac{\log_{b} (a) \cdot \log_{a} (b)}{\log (10)}$
32521	Evaluate	log base b of (b)^x	$\log_{b} ({(b)}^{x})$
32522	Evaluate	( log base 9 of 12x)/( log base 9 of 6x)	$\frac{\log_{9} (12 x)}{\log_{9} (6 x)}$
32523	Evaluate	log base 9 of (243)^(2/5)	$\log_{9} ({(243)}^{\frac{2}{5}})$
32524	Evaluate	log base 8 of (8)^79	$\log_{8} ({(8)}^{79})$
32525	Evaluate	( log base 8 of x)/( log base 8 of 2)	$\frac{\log_{8} (x)}{\log_{8} (2)}$
32526	Evaluate	log base 6 of (u^4*v)^5	$\log_{6} ({(u^{4} \cdot v)}^{5})$
32527	Evaluate	( log base 6 of square root of xy^3)/(2^3)	$\frac{\log_{6} (\sqrt{x} y^{3})}{2^{3}}$
32528	Evaluate	log base 7 of (7)^3	$\log_{7} ({(7)}^{3})$
32529	Evaluate	log base 7 of (7)^6	$\log_{7} ({(7)}^{6})$
32530	Evaluate	log base 8 of ((8y(x-5))/( fourth root of x))^3	$\log_{8} ({(\frac{8 y (x - 5)}{\sqrt[4]{x}})}^{3})$
32531	Evaluate	( log base 8 of 3)/4	$\frac{\log_{8} (3)}{4}$
32532	Evaluate	( log base 8 of 37)/9	$\frac{\log_{8} (37)}{9}$
32533	Evaluate	log base 8 of (3x)^4	$\log_{8} ({(3 x)}^{4})$
32534	Evaluate	log base 8 of (4)^( log of 1000)	$\log_{8} ({(4)}^{\log (1000)})$
32535	Evaluate	log base 8 of (4096)^3	$\log_{8} ({(4096)}^{3})$
32536	Evaluate	log base 6 of (x/36)^4	$\log_{6} ({(\frac{x}{36})}^{4})$
32537	Evaluate	( log base 6 of 11 square root of r)/s	$\frac{\log_{6} (11 \sqrt{r})}{s}$
32538	Evaluate	( log base 6 of 14)/3	$\frac{\log_{6} (14)}{3}$
32539	Evaluate	( log base 6 of 15)/( log base 6 of 6)	$\frac{\log_{6} (15)}{\log_{6} (6)}$
32540	Evaluate	log base 6 of (36)^7	$\log_{6} ({(36)}^{7})$
32541	Evaluate	( log base 6 of 5)/3+( log base 6 of 8)/6+( log base 6 of 11)/3	$\frac{\log_{6} (5)}{3} + \frac{\log_{6} (8)}{6} + \frac{\log_{6} (11)}{3}$
32542	Evaluate	log base 6 of (55)^10	$\log_{6} ({(55)}^{10})$
32543	Evaluate	log base 6 of (6)^10	$\log_{6} ({(6)}^{10})$
32544	Evaluate	log base 6 of (6)^15	$\log_{6} ({(6)}^{15})$
32545	Evaluate	log base 6 of (6)^2	$\log_{6} ({(6)}^{2})$
32546	Evaluate	log base 6 of (6)^3	$\log_{6} ({(6)}^{3})$
32547	Evaluate	log base 6 of (6)^40	$\log_{6} ({(6)}^{40})$
32548	Evaluate	log base 6 of (p)^5	$\log_{6} ({(p)}^{5})$
32549	Evaluate	log base 6 of (xy)^3	$\log_{6} ({(x y)}^{3})$
32550	Evaluate	log base 6 of (xy)^9	$\log_{6} ({(x y)}^{9})$
32551	Evaluate	log base 7 of (8/(3^5))^3	$\log_{7} ({(\frac{8}{3^{5}})}^{3})$
32552	Evaluate	log base 7 of (8^3*5)^2	$\log_{7} ({(8^{3} \cdot 5)}^{2})$
32553	Evaluate	( log base 7 of 2)/( log base 7 of 3)	$\frac{\log_{7} (2)}{\log_{7} (3)}$
32554	Evaluate	( log base 7 of 243)/( log base 7 of 3)	$\frac{\log_{7} (243)}{\log_{7} (3)}$
32555	Evaluate	( log base 7 of 25)/( log base 7 of 5)	$\frac{\log_{7} (25)}{\log_{7} (5)}$
32556	Evaluate	( log base 7 of 32)/( log base 7 of 2)	$\frac{\log_{7} (32)}{\log_{7} (2)}$
32557	Evaluate	( log base 7 of 45)/( log base 7 of 5)	$\frac{\log_{7} (45)}{\log_{7} (5)}$
32558	Evaluate	log base 7 of (7)^-0.89	$\log_{7} ({(7)}^{- 0.89})$
32559	Find the Roots (Zeros)	f(x)=x^2+3x+1	$f (x) = x^{2} + 3 x + 1$
32560	Evaluate	( natural log of e)/( natural log of 3 natural log of x-2)	$\frac{\ln (e)}{\ln (3 \ln (x - 2))}$
32561	Evaluate	log base h of (N)^3	$\log_{h} ({(N)}^{3})$
32562	Evaluate	( log base z of xy^z)/64	$\frac{\log_{z} (x y^{z})}{64}$
32563	Evaluate	( square root of natural log of 4)/( natural log of square root of 4)	$\frac{\sqrt{\ln (4)}}{\ln (\sqrt{4})}$
32564	Evaluate	0.15/(( natural log of 1/2)/22)	$\frac{0.15}{\frac{\ln (\frac{1}{2})}{22}}$
32565	Evaluate	(0.361(-1)+1.9)/((0.19(-1)+1)^3)-(1.9 natural log of 0.19(-1)+1)/((0.19(-1)+1)^2)	$\frac{0.361 (- 1) + 1.9}{{(0.19 (- 1) + 1)}^{3}} - \frac{1.9 \ln (0.19 (- 1) + 1)}{{(0.19 (- 1) + 1)}^{2}}$
32566	Evaluate	0.60(e)^((( natural log of 0.56/0.60)/30)(180))	$0.6 {(e)}^{(\frac{\ln (\frac{0.56}{0.6})}{30}) (180)}$
32567	Evaluate	1/0.01* natural log of 44/38	$\frac{1}{0.01} \cdot \ln (\frac{44}{38})$
32568	Evaluate	1/( log base 5 of 35)+1/( log base 7 of 35)	$\frac{1}{\log_{5} (35)} + \frac{1}{\log_{7} (35)}$
32569	Evaluate	1/0.0000000154* natural log of (0.0681+0.0391)/0.0681	$\frac{1}{0.00000001} \cdot \ln (\frac{0.0681 + 0.0391}{0.0681})$
32570	Evaluate	-1/0.002* natural log of 1220	$- \frac{1}{0.002} \cdot \ln (1220)$
32571	Evaluate	1/0.03* natural log of 78/(78-54)	$\frac{1}{0.03} \cdot \ln (\frac{78}{78 - 54})$
32572	Evaluate	1/(1.5410^-8) natural log of (0.0681+0.0391)/0.0681	$\frac{1}{1.54 \cdot 10^{- 8}} \cdot \ln (\frac{0.0681 + 0.0391}{0.0681})$
32573	Evaluate	1/(1+ log base c of ab)	$\frac{1}{1 + \log_{c} (a b)}$
32574	Evaluate	1/1690* natural log of 1/2	$\frac{1}{1690} \cdot \ln (\frac{1}{2})$
32575	Evaluate	1/(2 log base 5 of x-4 log base 5 of y- log base 5 of z)	$\frac{1}{2 \log_{5} (x) - 4 \log_{5} (y) - \log_{5} (z)}$
32576	Evaluate	1/2*( log base 3 of x+ log base 3 of y)-3 log base 3 of x+3	$\frac{1}{2} \cdot (\log_{3} (x) + \log_{3} (y)) - 3 \log_{3} (x + 3)$
32577	Evaluate	1/2*( log base 4 of s+ log base 4 of t)	$\frac{1}{2} \cdot (\log_{4} (s) + \log_{4} (t))$
32578	Evaluate	1/2*( log base 5 of x+ log base 5 of y)	$\frac{1}{2} \cdot (\log_{5} (x) + \log_{5} (y))$
32579	Evaluate	1/2*( log base 6 of x+ log base 6 of y)-5 log base 6 of x+8	$\frac{1}{2} \cdot (\log_{6} (x) + \log_{6} (y)) - 5 \log_{6} (x + 8)$
32580	Evaluate	1/2*( log base 7 of s+ log base 7 of t)	$\frac{1}{2} \cdot (\log_{7} (s) + \log_{7} (t))$
32581	Evaluate	1/2*( log base 7 of x+ log base 7 of y)-4 log base 7 of x+6	$\frac{1}{2} \cdot (\log_{7} (x) + \log_{7} (y)) - 4 \log_{7} (x + 6)$
32582	Evaluate	1/2*(4 natural log of a+ natural log of b-4 natural log of c)	$\frac{1}{2} \cdot (4 \ln (a) + \ln (b) - 4 \ln (c))$
32583	Evaluate	1/2*(4 natural log of x- natural log of y- natural log of z)	$\frac{1}{2} \cdot (4 \ln (x - \ln (y) - \ln (z)))$
32584	Evaluate	1/2*( natural log of x+2- natural log of x^2-4)	$\frac{1}{2} \cdot (\ln (x + 2) - \ln (x^{2} - 4))$
32585	Evaluate	1/2*( log of x+1-2 log of x-1-3 log of x)	$\frac{1}{2} \cdot (\log (x + 1) - 2 \log (x - 1) - 3 \log (x))$
32586	Evaluate	1/2*e^( natural log of 3-2 natural log of 5)	$\frac{1}{2} \cdot e^{\ln (3) - 2 \ln (5)}$
32587	Evaluate	1/2* natural log of (8)^2	$\frac{1}{2} \cdot \ln ({(8)}^{2})$
32588	Evaluate	1/2* log base 12 of 9+1/3* log base 12 of 7	$\frac{1}{2} \cdot \log_{12} (9) + \frac{1}{3} \cdot \log_{12} (7)$
32589	Evaluate	1/2* log base 3 of 27^2	$\frac{1}{2} \cdot \log_{3} (27^{2})$
32590	Evaluate	1/2* log base 3 of 9- log base 3 of 12+2 log base 3 of 6	$\frac{1}{2} \cdot \log_{3} (9) - \log_{3} (12) + 2 \log_{3} (6)$
32591	Evaluate	1/2* log base 6 of x+ log base 6 of y-3 log base 6 of z	$\frac{1}{2} \cdot \log_{6} (x) + \log_{6} (y) - 3 \log_{6} (z)$
32592	Evaluate	1/2* log base 7 of x-8- log base 7 of x	$\frac{1}{2} \cdot \log_{7} (x - 8) - \log_{7} (x)$
32593	Evaluate	1/2*( log base c of x+2 log base c of y-4 log base c of x)	$\frac{1}{2} \cdot (\log_{c} (x + 2) \log_{c} (y - 4) \log_{c} (x))$
32594	Evaluate	1/2* natural log of x-(2 natural log of x-1+ natural log of x+1)	$\frac{1}{2} \cdot \ln (x) - (2 \ln (x - 1) + \ln (x + 1))$
32595	Evaluate	1/2* natural log of x+7 natural log of y-2 natural log of z	$\frac{1}{2} \cdot \ln (x) + 7 \ln (y) - 2 \ln (z)$
32596	Evaluate	1/2* log of b^5	$\frac{1}{2} \cdot \log (b^{5})$
32597	Evaluate	1/3* log base 3 of x-1-3	$\frac{1}{3} \cdot \log_{3} (x - 1) - 3$
32598	Evaluate	1/3* log base 49 of 7	$\frac{1}{3} \cdot \log_{49} (7)$
32599	Evaluate	1/3* log base 5 of 125	$\frac{1}{3} \cdot \log_{5} (125)$
32600	Evaluate	1/3* log base m of z+6 log base m of x- log base m of w	$\frac{1}{3} \cdot \log_{m} (z) + 6 \log_{m} (x) - \log_{m} (w)$