Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
36501	Expand the Logarithmic Expression	natural log of (x^3z^-7)/(y^-8)	$\ln (\frac{x^{3} z^{- 7}}{y^{- 8}})$
36502	Expand the Logarithmic Expression	natural log of (x^2)/(yz^3)	$\ln (\frac{x^{2}}{y z^{3}})$
36503	Expand the Logarithmic Expression	natural log of (x^2-1)/(x^3)	$\ln (\frac{x^{2} - 1}{x^{3}})$
36504	Expand the Logarithmic Expression	natural log of (x^2-1)/(x^7)	$\ln (\frac{x^{2} - 1}{x^{7}})$
36505	Expand the Logarithmic Expression	natural log of (x^2-16)/(x^2)	$\ln (\frac{x^{2} - 16}{x^{2}})$
36506	Expand the Logarithmic Expression	natural log of ( cube root of x^4-81)/((x+16) square root of x-3)	$\ln (\frac{\sqrt[3]{x^{4} - 81}}{(x + 16) \sqrt{x - 3}})$
36507	Expand the Logarithmic Expression	natural log of 1/(e^(5x))	$\ln (\frac{1}{e^{5 x}})$
36508	Expand the Logarithmic Expression	natural log of 1/(e^8)	$\ln (\frac{1}{e^{8}})$
36509	Expand the Logarithmic Expression	natural log of 1/(e^9)	$\ln (\frac{1}{e^{9}})$
36510	Expand the Logarithmic Expression	natural log of 1/( square root of e^3)	$\ln (\frac{1}{\sqrt{e^{3}}})$
36511	Expand the Logarithmic Expression	natural log of 1/( square root of e^7)	$\ln (\frac{1}{\sqrt{e^{7}}})$
36512	Expand the Logarithmic Expression	natural log of ( square root of 7)/( cube root of 3)	$\ln (\frac{\sqrt{7}}{\sqrt[3]{3}})$
36513	Expand the Logarithmic Expression	natural log of 1/x	$\ln (\frac{1}{x})$
36514	Expand the Logarithmic Expression	natural log of (10e^(3x))/(9x)	$\ln (\frac{10 e^{3 x}}{9 x})$
36515	Expand the Logarithmic Expression	natural log of 10^(x-2)	$\ln (10^{x - 2})$
36516	Expand the Logarithmic Expression	natural log of (100x^5 cube root of 5-x)/(3(x+4)^2)	$\ln (\frac{100 x^{5} \sqrt[3]{5 - x}}{3 {(x + 4)}^{2}})$
36517	Expand the Logarithmic Expression	natural log of (11x^2)/(y^5)	$\ln (\frac{11 x^{2}}{y^{5}})$
36518	Expand the Logarithmic Expression	natural log of (11x^2)/(9 square root of yt^5)	$\ln (\frac{11 x^{2}}{9 \sqrt{y} t^{5}})$
36519	Expand the Logarithmic Expression	natural log of (11x^3)/(y^9)	$\ln (\frac{11 x^{3}}{y^{9}})$
36520	Expand the Logarithmic Expression	natural log of 11/e	$\ln (\frac{11}{e})$
36521	Expand the Logarithmic Expression	natural log of 11^3 square root of 7*12	$\ln (11^{3} \sqrt{7 \cdot 12})$
36522	Expand the Logarithmic Expression	natural log of (13x^8)/(y^8)	$\ln (\frac{13 x^{8}}{y^{8}})$
36523	Expand the Logarithmic Expression	natural log of 14/11	$\ln (\frac{14}{11})$
36524	Expand the Logarithmic Expression	natural log of 18/( square root of x^6+1)	$\ln (\frac{18}{\sqrt{x^{6} + 1}})$
36525	Expand the Logarithmic Expression	natural log of (2x^3)/(3y)	$\ln (\frac{2 x^{3}}{3 y})$
36526	Expand the Logarithmic Expression	natural log of (3e)/(2 square root of x)	$\ln (\frac{3 e}{2 \sqrt{x}})$
36527	Expand the Logarithmic Expression	natural log of (3x square root of 1+4x)/((x-4)^9)	$\ln (\frac{3 x \sqrt{1 + 4 x}}{{(x - 4)}^{9}})$
36528	Expand the Logarithmic Expression	natural log of (3x square root of 1+5x)/((x-7)^9)	$\ln (\frac{3 x \sqrt{1 + 5 x}}{{(x - 7)}^{9}})$
36529	Expand the Logarithmic Expression	natural log of (3x square root of 1+7x)/((x-4)^10)	$\ln (\frac{3 x \sqrt{1 + 7 x}}{{(x - 4)}^{10}})$
36530	Expand the Logarithmic Expression	natural log of (3x-2)/(x+6)	$\ln (\frac{3 x - 2}{x + 6})$
36531	Expand the Logarithmic Expression	natural log of (4df^5)/( eighth root of 1-3d)	$\ln (\frac{4 d f^{5}}{\sqrt[8]{1 - 3 d}})$
36532	Expand the Logarithmic Expression	natural log of (4x^3)/( square root of y(x-2)^6)	$\ln (\frac{4 x^{3}}{\sqrt{y} {(x - 2)}^{6}})$
36533	Expand the Logarithmic Expression	natural log of 4/3	$\ln (\frac{4}{3})$
36534	Expand the Logarithmic Expression	natural log of 4/(9x^9y)	$\ln (\frac{4}{9 x^{9} y})$
36535	Expand the Logarithmic Expression	natural log of (5e^3x)/( square root of x+e)	$\ln (\frac{5 e^{3} x}{\sqrt{x + e}})$
36536	Expand the Logarithmic Expression	natural log of (5 square root of 3)/( cube root of 7)	$\ln (\frac{5 \sqrt{3}}{\sqrt[3]{7}})$
36537	Expand the Logarithmic Expression	natural log of (5 square root of x)/6	$\ln (\frac{5 \sqrt{x}}{6})$
36538	Expand the Logarithmic Expression	natural log of (5x^3)/(y^5)	$\ln (\frac{5 x^{3}}{y^{5}})$
36539	Expand the Logarithmic Expression	natural log of (5x^3)/y	$\ln (\frac{5 x^{3}}{y})$
36540	Expand the Logarithmic Expression	natural log of (5x^5 square root of x^3-4)/(x^2)	$\ln (\frac{5 x^{5} \sqrt{x^{3} - 4}}{x^{2}})$
36541	Expand the Logarithmic Expression	natural log of 2/3	$\ln (\frac{2}{3})$
36542	Expand the Logarithmic Expression	natural log of 2/5	$\ln (\frac{2}{5})$
36543	Expand the Logarithmic Expression	natural log of 2/(7x^7y)	$\ln (\frac{2}{7 x^{7} y})$
36544	Expand the Logarithmic Expression	natural log of 292/760	$\ln (\frac{292}{760})$
36545	Expand the Logarithmic Expression	natural log of (2pi)/(3q)	$\ln (\frac{2 π}{3 q})$
36546	Expand the Logarithmic Expression	natural log of (2x square root of 1+6x)/((x-7)^15)	$\ln (\frac{2 x \sqrt{1 + 6 x}}{{(x - 7)}^{15}})$
36547	Expand the Logarithmic Expression	natural log of (3a^4b^7c)/( fourth root of b-9)	$\ln (\frac{3 a^{4} b^{7} c}{\sqrt[4]{b - 9}})$
36548	Expand the Logarithmic Expression	natural log of (3e^(5x-7)(3x+1)^4)/((x-2) cube root of x)	$\ln (\frac{3 e^{5 x - 7} {(3 x + 1)}^{4}}{(x - 2) \sqrt[3]{x}})$
36549	Expand the Logarithmic Expression	natural log of (3 square root of c)/(a^3b^2)	$\ln (\frac{3 \sqrt{c}}{a^{3} b^{2}})$
36550	Expand the Logarithmic Expression	natural log of (63x^2)/5	$\ln (\frac{63 x^{2}}{5})$
36551	Expand the Logarithmic Expression	natural log of (6x square root of 1+2x)/(x-6)	$\ln (\frac{6 x \sqrt{1 + 2 x}}{x - 6})$
36552	Expand the Logarithmic Expression	natural log of (7 square root of z)/((y-2)^3)	$\ln (\frac{7 \sqrt{z}}{{(y - 2)}^{3}})$
36553	Expand the Logarithmic Expression	natural log of 7/0	$\ln (\frac{7}{0})$
36554	Expand the Logarithmic Expression	natural log of 7/(4x^4y)	$\ln (\frac{7}{4 x^{4} y})$
36555	Expand the Logarithmic Expression	natural log of (7x square root of 1+4x)/((x-2)^6)	$\ln (\frac{7 x \sqrt{1 + 4 x}}{{(x - 2)}^{6}})$
36556	Expand the Logarithmic Expression	natural log of (7x square root of 1+6x)/((x-8)^4)	$\ln (\frac{7 x \sqrt{1 + 6 x}}{{(x - 8)}^{4}})$
36557	Expand the Logarithmic Expression	natural log of (7x)/3	$\ln (\frac{7 x}{3})$
36558	Expand the Logarithmic Expression	natural log of 8000/(14414/( natural log of 0.8))	$\ln (\frac{8000}{\frac{14414}{\ln (0.8)}})$
36559	Expand the Logarithmic Expression	natural log of (9x^8)/((x+5)^8)	$\ln (\frac{9 x^{8}}{{(x + 5)}^{8}})$
36560	Expand the Logarithmic Expression	natural log of 9/(2x^2y)	$\ln (\frac{9}{2 x^{2} y})$
36561	Expand the Logarithmic Expression	natural log of 9/(5x^5y)	$\ln (\frac{9}{5 x^{5} y})$
36562	Expand the Logarithmic Expression	natural log of 9/(7x^7y)	$\ln (\frac{9}{7 x^{7} y})$
36563	Expand the Logarithmic Expression	natural log of 9/(8x^8y)	$\ln (\frac{9}{8 x^{8} y})$
36564	Expand the Logarithmic Expression	natural log of a^2b^5	$\ln (a^{2} b^{5})$
36565	Expand the Logarithmic Expression	natural log of A^3* square root of B	$\ln (A^{3} \cdot \sqrt{B})$
36566	Expand the Logarithmic Expression	natural log of a^5 square root of bc^5	$\ln (a^{5} \sqrt{b c^{5}})$
36567	Expand the Logarithmic Expression	natural log of b/a	$\ln (\frac{b}{a})$
36568	Expand the Logarithmic Expression	natural log of b^2* cube root of a	$\ln (b^{2} \cdot \sqrt[3]{a})$
36569	Expand the Logarithmic Expression	natural log of (bx)/c	$\ln (\frac{b x}{c})$
36570	Expand the Logarithmic Expression	natural log of (e^x)/(5e^(-x))	$\ln (\frac{e^{x}}{5 e^{- x}})$
36571	Expand the Logarithmic Expression	natural log of (k^5)/(m^3)	$\ln (\frac{k^{5}}{m^{3}})$
36572	Expand the Logarithmic Expression	natural log of (m^5 fourth root of b^3)/(p^3r)	$\ln (\frac{m^{5} \sqrt[4]{b^{3}}}{p^{3} r})$
36573	Expand the Logarithmic Expression	natural log of (v(x-2))/(y^3z^3)	$\ln (\frac{v (x - 2)}{y^{3} z^{3}})$
36574	Expand the Logarithmic Expression	natural log of (v(x-1))/(x^2)	$\ln (\frac{v (x - 1)}{x^{2}})$
36575	Expand the Logarithmic Expression	natural log of ( square root of x^2+1)/(x^4(2x-1)^3)	$\ln (\frac{\sqrt{x^{2} + 1}}{x^{4} {(2 x - 1)}^{3}})$
36576	Expand the Logarithmic Expression	natural log of ( square root of x^2+4)/(y*(x-1)^6)	$\ln (\frac{\sqrt{x^{2} + 4}}{y \cdot {(x - 1)}^{6}})$
36577	Expand the Logarithmic Expression	natural log of ( square root of 2x^(3/2))/(e^2)	$\ln (\frac{\sqrt{2} x^{\frac{3}{2}}}{e^{2}})$
36578	Expand the Logarithmic Expression	natural log of ( square root of 2)/(xy)	$\ln (\frac{\sqrt{2}}{x y})$
36579	Expand the Logarithmic Expression	natural log of ( square root of 3x-5)/(y^2)	$\ln (\frac{\sqrt{3 x - 5}}{y^{2}})$
36580	Expand the Logarithmic Expression	natural log of ( square root of 3x-5)/7	$\ln (\frac{\sqrt{3 x - 5}}{7})$
36581	Expand the Logarithmic Expression	natural log of ( square root of 4+x^2)/x	$\ln (\frac{\sqrt{4 + x^{2}}}{x})$
36582	Expand the Logarithmic Expression	natural log of ( square root of 5x-7)/3	$\ln (\frac{\sqrt{5 x - 7}}{3})$
36583	Expand the Logarithmic Expression	natural log of ( square root of 81-x^2)/((x-7)(x+7)^(3/2))	$\ln (\frac{\sqrt{81 - x^{2}}}{(x - 7) {(x + 7)}^{\frac{3}{2}}})$
36584	Expand the Logarithmic Expression	natural log of ( square root of x(x+1))/((x-1)^2)	$\ln (\frac{\sqrt{x} (x + 1)}{{(x - 1)}^{2}})$
36585	Expand the Logarithmic Expression	natural log of ( square root of x*y^5)/((z+1)^4)	$\ln (\frac{\sqrt{x} \cdot y^{5}}{{(z + 1)}^{4}})$
36586	Expand the Logarithmic Expression	natural log of ( square root of x)/(8y^3)	$\ln (\frac{\sqrt{x}}{8 y^{3}})$
36587	Expand the Logarithmic Expression	natural log of ( square root of x-1)/( cube root of 2x-3)	$\ln (\frac{\sqrt{x - 1}}{\sqrt[3]{2 x - 3}})$
36588	Expand the Logarithmic Expression	natural log of ( square root of x-43)/x	$\ln (\frac{\sqrt{x - 43}}{x})$
36589	Expand the Logarithmic Expression	natural log of ( square root of xy)/(e^3z)	$\ln (\frac{\sqrt{x y}}{e^{3} z})$
36590	Expand the Logarithmic Expression	natural log of (e^3 fourth root of x^2)/( cube root of y)	$\ln (\frac{e^{3} \sqrt[4]{x^{2}}}{\sqrt[3]{y}})$
36591	Expand the Logarithmic Expression	natural log of (e^3)/(xy^2)	$\ln (\frac{e^{3}}{x y^{2}})$
36592	Expand the Logarithmic Expression	natural log of (e^3)/15	$\ln (\frac{e^{3}}{15})$
36593	Expand the Logarithmic Expression	natural log of 2/(e^x)	$\ln (\frac{2}{e^{x}})$
36594	Expand the Logarithmic Expression	natural log of x/(5y)	$\ln (\frac{x}{5 y})$
36595	Expand the Logarithmic Expression	natural log of (e^3)/9	$\ln (\frac{e^{3}}{9})$
36596	Expand the Logarithmic Expression	natural log of (e^4)/12	$\ln (\frac{e^{4}}{12})$
36597	Expand the Logarithmic Expression	natural log of (e^4)/2	$\ln (\frac{e^{4}}{2})$
36598	Expand the Logarithmic Expression	natural log of (e^4)/4	$\ln (\frac{e^{4}}{4})$
36599	Expand the Logarithmic Expression	natural log of (e^4)/5	$\ln (\frac{e^{4}}{5})$
36600	Expand the Logarithmic Expression	natural log of (e^4)/9	$\ln (\frac{e^{4}}{9})$