Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
36401	Expand the Logarithmic Expression	natural log of ((x-2)^5 square root of x+1)/(x^4)	$\ln (\frac{{(x - 2)}^{5} \sqrt{x + 1}}{x^{4}})$
36402	Expand the Logarithmic Expression	natural log of (26/19)/0.09	$\ln (\frac{\frac{26}{19}}{0.09})$
36403	Expand the Logarithmic Expression	natural log of (a^2b^8)/(c^6)	$\ln (\frac{a^{2} b^{8}}{c^{6}})$
36404	Expand the Logarithmic Expression	natural log of (a^-2)/(b^-4c^5)	$\ln (\frac{a^{- 2}}{b^{- 4} c^{5}})$
36405	Expand the Logarithmic Expression	natural log of (a^3)/(b^4c^4)	$\ln (\frac{a^{3}}{b^{4} c^{4}})$
36406	Expand the Logarithmic Expression	natural log of (a^4*b)/( fourth root of c)	$\ln (\frac{a^{4} \cdot b}{\sqrt[4]{c}})$
36407	Expand the Logarithmic Expression	natural log of (a^5b^7)/(c^9)	$\ln (\frac{a^{5} b^{7}}{c^{9}})$
36408	Expand the Logarithmic Expression	natural log of (ab^3)/( square root of c^2)	$\ln (\frac{a b^{3}}{\sqrt{c^{2}}})$
36409	Expand the Logarithmic Expression	natural log of (e^( square root of y)* square root of x^3)/(y^2)	$\ln (\frac{e^{\sqrt{y}} \cdot \sqrt{x^{3}}}{y^{2}})$
36410	Expand the Logarithmic Expression	natural log of (e^4x^2)/( square root of y)	$\ln (\frac{e^{4} x^{2}}{\sqrt{y}})$
36411	Expand the Logarithmic Expression	natural log of (e^7)/8	$\ln (\frac{e^{7}}{8})$
36412	Expand the Logarithmic Expression	natural log of ( square root of x+5 fifth root of x-2)/((x+1)^2)	$\ln (\frac{\sqrt{x + 5} \sqrt[5]{x - 2}}{{(x + 1)}^{2}})$
36413	Expand the Logarithmic Expression	natural log of (x^2(2x-1))/((2x+1)^(3/2))	$\ln (\frac{x^{2} (2 x - 1)}{{(2 x + 1)}^{\frac{3}{2}}})$
36414	Expand the Logarithmic Expression	natural log of (x^2sin(x)^3)/( square root of x^2+1)	$\ln (\frac{x^{2} \sin^{3} (x)}{\sqrt{x^{2}} + 1})$
36415	Expand the Logarithmic Expression	natural log of (x^2+1)^2( square root of x-1)	$\ln ({(x^{2} + 1)}^{2} (\sqrt{x - 1}))$
36416	Expand the Logarithmic Expression	natural log of (x^3 square root of x-1)/(3x+4)	$\ln (\frac{x^{3} \sqrt{x - 1}}{3 x + 4})$
36417	Expand the Logarithmic Expression	natural log of (x^3y^5)/(z^8)	$\ln (\frac{x^{3} y^{5}}{z^{8}})$
36418	Expand the Logarithmic Expression	natural log of (x^3-1)/(x^7)	$\ln (\frac{x^{3} - 1}{x^{7}})$
36419	Expand the Logarithmic Expression	natural log of (x^3w)/(yz^7)	$\ln (\frac{x^{3} w}{y z^{7}})$
36420	Expand the Logarithmic Expression	natural log of (x^3y)/(z^2)	$\ln (\frac{x^{3} y}{z^{2}})$
36421	Expand the Logarithmic Expression	natural log of (x^4v(p^9q^7))/(e^8)	$\ln (\frac{x^{4} v (p^{9} q^{7})}{e^{8}})$
36422	Expand the Logarithmic Expression	natural log of ((1-p)d)/( sixth root of 2+5r)	$\ln (\frac{(1 - p) d}{\sqrt[6]{2 + 5 r}})$
36423	Expand the Logarithmic Expression	natural log of ((2x)11 root of 1+7x)/((x-9)^9)	$\ln (\frac{(2 x) \sqrt[11]{1 + 7 x}}{{(x - 9)}^{9}})$
36424	Expand the Logarithmic Expression	natural log of (2x)/y	$\ln (\frac{2 x}{y})$
36425	Expand the Logarithmic Expression	natural log of (3x^4)/((zy)^2)	$\ln (\frac{3 x^{4}}{{(z y)}^{2}})$
36426	Expand the Logarithmic Expression	natural log of (4x^4)/(y^4)	$\ln (\frac{4 x^{4}}{y^{4}})$
36427	Expand the Logarithmic Expression	natural log of ((4x^5-x-1) square root of x-7)/((x^2+1)^3)	$\ln (\frac{(4 x^{5} - x - 1) \sqrt{x - 7}}{{(x^{2} + 1)}^{3}})$
36428	Expand the Logarithmic Expression	natural log of 0.80/-0.15	$\ln (\frac{0.8}{- 0.15})$
36429	Expand the Logarithmic Expression	natural log of ((x^2-x-2)/((x+3)^2))^(1/3)	$\ln ({(\frac{x^{2} - x - 2}{{(x + 3)}^{2}})}^{\frac{1}{3}})$
36430	Expand the Logarithmic Expression	63000 natural log of 6*3.1+7	$63000 \ln (6 \cdot 3.1 + 7)$
36431	Expand the Logarithmic Expression	6 natural log of square root of x^3-5 natural log of fifth root of y^4	$6 \ln (\sqrt{x^{3}} - 5) \ln (\sqrt[5]{y^{4}})$
36432	Expand the Logarithmic Expression	6 natural log of 8x-1/2* natural log of y-3	$6 \ln (8 x) - \frac{1}{2} \cdot \ln (y - 3)$
36433	Expand the Logarithmic Expression	6 natural log of u-2 natural log of v	$6 \ln (u - 2 \ln (v))$
36434	Expand the Logarithmic Expression	6 natural log of x+6-9 natural log of x	$6 \ln (x + 6) - 9 \ln (x)$
36435	Expand the Logarithmic Expression	6 log of 36x^3	$6 \log (36 x^{3})$
36436	Expand the Logarithmic Expression	6 log of 5x	$6 \log (5 x)$
36437	Expand the Logarithmic Expression	6 log of 6*9	$6 \log (6) \cdot 9$
36438	Expand the Logarithmic Expression	6 log of 811+12 log of 82	$6 \log (8) \cdot 11 + 12 \log (8) \cdot 2$
36439	Expand the Logarithmic Expression	6x natural log of 18	$6 x \ln (18)$
36440	Expand the Logarithmic Expression	2 log of 2x- log of 4x	$2 \log (2 x - \log (4 x))$
36441	Expand the Logarithmic Expression	2x+ natural log of x	$2 x + \ln (x)$
36442	Expand the Logarithmic Expression	-3 log base 8 of 4x	$- 3 \log_{8} (4 x)$
36443	Expand the Logarithmic Expression	3 log base h of 1/b	$3 \log_{h} (\frac{1}{b})$
36444	Expand the Logarithmic Expression	3 log base x of 2	$3 \log_{x} (2)$
36445	Expand the Logarithmic Expression	3 natural log of e^9- natural log of e^9	$3 \ln (e^{9}) - \ln (e^{9})$
36446	Expand the Logarithmic Expression	3 natural log of 2x-5	$3 \ln (2 x - 5)$
36447	Expand the Logarithmic Expression	3 natural log of 7x	$3 \ln (7 x)$
36448	Expand the Logarithmic Expression	3 natural log of x+1/2* natural log of y-2	$3 \ln (x) + \frac{1}{2} \cdot \ln (y - 2)$
36449	Expand the Logarithmic Expression	3 log of 100	$3 \log (100)$
36450	Expand the Logarithmic Expression	3 log of 2x	$3 \log (2 x)$
36451	Expand the Logarithmic Expression	3 log of 2x-1	$3 \log (2 x - 1)$
36452	Expand the Logarithmic Expression	3 log of 3	$3 \log (3)$
36453	Expand the Logarithmic Expression	4.6 natural log of x^2	$4.6 \ln (x^{2})$
36454	Expand the Logarithmic Expression	4 log base 0.333 of 3	$4 \log_{0.333} (3)$
36455	Expand the Logarithmic Expression	4 log base 2 of 1/8	$4 \log_{2} (\frac{1}{8})$
36456	Expand the Logarithmic Expression	4 log base 2 of 16-2 natural log of e^3	$4 \log_{2} (16) - 2 \ln (e^{3})$
36457	Expand the Logarithmic Expression	4 log base 3 of x-1/3* log base 3 of x+6	$4 \log_{3} (x - \frac{1}{3} \cdot \log_{3} (x + 6))$
36458	Expand the Logarithmic Expression	4 log base 5 of square root of 3x-5- log base 5 of 2/x+ log base 5 of 2	$4 \log_{5} (\sqrt{3 x - 5}) - \log_{5} (\frac{2}{x}) + \log_{5} (2)$
36459	Expand the Logarithmic Expression	4 log base 5 of 652	$4 \log_{5} (652)$
36460	Expand the Logarithmic Expression	4 log base 7 of u+9 log base 7 of v	$4 \log_{7} (u + 9) \log_{7} (v)$
36461	Expand the Logarithmic Expression	4 log base 9 of 11-24 log base 9 of 10	$4 \log_{9} (11 - 24 \log_{9} (10))$
36462	Expand the Logarithmic Expression	4 log base a of 5x^9-1/7* log base a of 2x+5	$4 \log_{a} (5 x^{9}) - \frac{1}{7} \cdot \log_{a} (2 x + 5)$
36463	Expand the Logarithmic Expression	4 log base a of q-3/2* log base a of r+1/3* log base a of f-6 log base a of p	$4 \log_{a} (q - \frac{3}{2} \cdot \log_{a} (r + \frac{1}{3} \cdot \log_{a} (f - 6 \log_{a} (p))))$
36464	Expand the Logarithmic Expression	400 log of 4	$400 \log (4)$
36465	Expand the Logarithmic Expression	4 natural log of square root of x^3-5 natural log of fifth root of y^4	$4 \ln (\sqrt{x^{3}} - 5) \ln (\sqrt[5]{y^{4}})$
36466	Expand the Logarithmic Expression	4 natural log of 2	$4 \ln (2)$
36467	Expand the Logarithmic Expression	4 natural log of 2+0.5 natural log of 9- natural log of 6	$4 \ln (2) + 0.5 \ln (9) - \ln (6)$
36468	Expand the Logarithmic Expression	4 natural log of 2x	$4 \ln (2 x)$
36469	Expand the Logarithmic Expression	4 natural log of c	$4 \ln (c)$
36470	Expand the Logarithmic Expression	4 log of 4	$4 \log (4)$
36471	Expand the Logarithmic Expression	4 log of 400	$4 \log (400)$
36472	Expand the Logarithmic Expression	4 log of 49-x^2-( log of 7+x+ log of 7-x)	$4 \log (49 - x^{2}) - (\log (7 + x) + \log (7 - x))$
36473	Expand the Logarithmic Expression	4 log of x-6 log of x+2	$4 \log (x - 6 \log (x + 2))$
36474	Expand the Logarithmic Expression	5( log base 6 of x+2 log base 6 of y-5 log base 6 of z)	$5 (\log_{6} (x) + 2 \log_{6} (y) - 5 \log_{6} (z))$
36475	Expand the Logarithmic Expression	(5( natural log of 1/3))/( natural log of 11/15)	$\frac{5 (\ln (\frac{1}{3}))}{\ln (\frac{11}{15})}$
36476	Expand the Logarithmic Expression	5 log of x	$5 \log (x)$
36477	Expand the Logarithmic Expression	5 log base 4 of (a^2b)/(n^3)	$5 \log_{4} (\frac{a^{2} b}{n^{3}})$
36478	Expand the Logarithmic Expression	5 log base 5 of 12	$5 \log_{5} (12)$
36479	Expand the Logarithmic Expression	5 log base 5 of 3	$5 \log_{5} (3)$
36480	Expand the Logarithmic Expression	5 log base 5 of 72	$5 \log_{5} (72)$
36481	Expand the Logarithmic Expression	5 log base 7 of x-2	$5 \log_{7} (x - 2)$
36482	Expand the Logarithmic Expression	5 log base b of q- log base b of r	$5 \log_{b} (q) - \log_{b} (r)$
36483	Expand the Logarithmic Expression	6 log base 7 of cube root of y	$6 \log_{7} (\sqrt[3]{y})$
36484	Expand the Logarithmic Expression	6.1+ log of b/c	$6.1 + \log (\frac{b}{c})$
36485	Expand the Logarithmic Expression	6 log base 7 of square root of 6x-7- log base 7 of 4/x+ log base 7 of 4	$6 \log_{7} (\sqrt{6 x - 7}) - \log_{7} (\frac{4}{x}) + \log_{7} (4)$
36486	Expand the Logarithmic Expression	6 log base 9 of cube root of y	$6 \log_{9} (\sqrt[3]{y})$
36487	Expand the Logarithmic Expression	6 log base a of q-5/2 log base a of r+1/6 log base a of f-4 log base a of P	$6 \log_{a} (q - \frac{5}{2}) \log_{a} (r + \frac{1}{6}) \log_{a} (f - 4) \log_{a} (P)$
36488	Expand the Logarithmic Expression	60e^((1/1690* natural log of 1/2)(400))	$60 e^{(\frac{1}{1690} \cdot \ln (\frac{1}{2})) (400)}$
36489	Expand the Logarithmic Expression	natural log of (xy^5)/(z^2)	$\ln (\frac{x y^{5}}{z^{2}})$
36490	Expand the Logarithmic Expression	natural log of (xy^6)/(z^6)	$\ln (\frac{x y^{6}}{z^{6}})$
36491	Expand the Logarithmic Expression	natural log of (xy^9)/(z^4)	$\ln (\frac{x y^{9}}{z^{4}})$
36492	Expand the Logarithmic Expression	natural log of (y^2)/(z square root of x^2+25)	$\ln (\frac{y^{2}}{z \sqrt{x^{2} + 25}})$
36493	Expand the Logarithmic Expression	natural log of (x^2-4)/(x^6)	$\ln (\frac{x^{2} - 4}{x^{6}})$
36494	Expand the Logarithmic Expression	natural log of (x^4sin(x)^5)/( square root of x^4+1)	$\ln (\frac{x^{4} \sin^{5} (x)}{\sqrt{x^{4} + 1}})$
36495	Expand the Logarithmic Expression	natural log of (x^4 square root of pq^5)/(e^6)	$\ln (\frac{x^{4} \sqrt{p q^{5}}}{e^{6}})$
36496	Expand the Logarithmic Expression	natural log of (x^4 square root of pq^7)/(e^3)	$\ln (\frac{x^{4} \sqrt{p q^{7}}}{e^{3}})$
36497	Expand the Logarithmic Expression	natural log of (x^4 square root of x^2-4)/( cube root of x^4+5)	$\ln (\frac{x^{4} \sqrt{x^{2} - 4}}{\sqrt[3]{x^{4} + 5}})$
36498	Expand the Logarithmic Expression	natural log of (x^4 square root of x-2)/(7x+3)	$\ln (\frac{x^{4} \sqrt{x - 2}}{7 x + 3})$
36499	Expand the Logarithmic Expression	natural log of (x^3 square root of x^2+1)/(x+1)	$\ln (\frac{x^{3} \sqrt{x^{2} + 1}}{x + 1})$
36500	Expand the Logarithmic Expression	natural log of (x^3 square root of x+8)/( seventh root of x^2+2x+1)	$\ln (\frac{x^{3} \sqrt{x + 8}}{\sqrt[7]{x^{2} + 2 x + 1}})$