Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
37301	Expand the Logarithmic Expression	natural log of fifth root of (4x^2-1)/(4x^(2+1))	$\ln (\sqrt[5]{\frac{4 x^{2} - 1}{4 x^{2 + 1}}})$
37302	Expand the Logarithmic Expression	natural log of e^(-0.026x)	$\ln (e^{- 0.026 x})$
37303	Expand the Logarithmic Expression	natural log of e^(13x)	$\ln (e^{13 x})$
37304	Expand the Logarithmic Expression	natural log of e^(1-x)	$\ln (e^{1 - x})$
37305	Expand the Logarithmic Expression	natural log of e^2p- natural log of q^3	$\ln (e^{2} p) - \ln (q^{3})$
37306	Expand the Logarithmic Expression	natural log of e^(2+w)	$\ln (e^{2 + w})$
37307	Expand the Logarithmic Expression	natural log of e^(2t+3)	$\ln (e^{2 t + 3})$
37308	Expand the Logarithmic Expression	natural log of e^(-2x)(x-1)^3(x^2+1)^-2	$\ln (e^{- 2 x} {(x - 1)}^{3} {(x^{2} + 1)}^{- 2})$
37309	Expand the Logarithmic Expression	natural log of e^(2x)-e^x	$\ln (e^{2 x} - e^{x})$
37310	Expand the Logarithmic Expression	natural log of e^(3x^2)	$\ln (e^{3 x^{2}})$
37311	Expand the Logarithmic Expression	natural log of e^(3x)(x^2+1)	$\ln (e^{3 x} (x^{2} + 1))$
37312	Expand the Logarithmic Expression	natural log of (5x^8)/((x+7)^3)	$\ln (\frac{5 x^{8}}{{(x + 7)}^{3}})$
37313	Expand the Logarithmic Expression	natural log of (5y^2)/(3x^3)	$\ln (\frac{5 y^{2}}{3 x^{3}})$
37314	Expand the Logarithmic Expression	natural log of 5/( square root of e^5)	$\ln (\frac{5}{\sqrt{e^{5}}})$
37315	Expand the Logarithmic Expression	natural log of 5/2	$\ln (\frac{5}{2})$
37316	Expand the Logarithmic Expression	natural log of 5^2	$\ln (5^{2})$
37317	Expand the Logarithmic Expression	natural log of 5^(2x)	$\ln (5^{2 x})$
37318	Expand the Logarithmic Expression	natural log of (5x square root of 1+3x)/((x+4)^3)	$\ln (\frac{5 x \sqrt{1 + 3 x}}{{(x + 4)}^{3}})$
37319	Expand the Logarithmic Expression	natural log of (5x square root of 1-3x)/((x-4)^3)	$\ln (\frac{5 x \sqrt{1 - 3 x}}{{(x - 4)}^{3}})$
37320	Expand the Logarithmic Expression	natural log of (5x)/( cube root of x^2+1)	$\ln (\frac{5 x}{\sqrt[3]{x^{2} + 1}})$
37321	Expand the Logarithmic Expression	natural log of (6 square root of x-3)/(7x^3)	$\ln (\frac{6 \sqrt{x - 3}}{7 x^{3}})$
37322	Expand the Logarithmic Expression	natural log of (6x^4)/((x^2+16)^2)	$\ln (\frac{6 x^{4}}{{(x^{2} + 16)}^{2}})$
37323	Graph	f(x) = cube root of -x	$f (x) = \sqrt[3]{- x}$
37324	Expand the Logarithmic Expression	natural log of e^42	$\ln (e^{42})$
37325	Expand the Logarithmic Expression	natural log of e^5x^2	$\ln (e^{5}) x^{2}$
37326	Expand the Logarithmic Expression	natural log of (3x^2)/( cube root of x^2-1)	$\ln (\frac{3 x^{2}}{\sqrt[3]{x^{2} - 1}})$
37327	Expand the Logarithmic Expression	natural log of (3x^2)/(y^3)	$\ln (\frac{3 x^{2}}{y^{3}})$
37328	Expand the Logarithmic Expression	natural log of (3x^2y)/( cube root of z)	$\ln (\frac{3 x^{2} y}{\sqrt[3]{z}})$
37329	Expand the Logarithmic Expression	natural log of 3/(e^2)	$\ln (\frac{3}{e^{2}})$
37330	Expand the Logarithmic Expression	natural log of 3/(2x^2y)	$\ln (\frac{3}{2 x^{2} y})$
37331	Expand the Logarithmic Expression	natural log of 3/4	$\ln (\frac{3}{4})$
37332	Expand the Logarithmic Expression	natural log of e^(8x)	$\ln (e^{8 x})$
37333	Expand the Logarithmic Expression	natural log of e^(cos(x))*tan(x)^2	$\ln (e^{\cos (x)} \cdot \tan^{2} (x))$
37334	Expand the Logarithmic Expression	natural log of -e^(-Nx)	$\ln (- e^{- N x})$
37335	Expand the Logarithmic Expression	natural log of square root of (x^4y)/z	$\ln (\sqrt{\frac{x^{4} y}{z}})$
37336	Expand the Logarithmic Expression	natural log of square root of ab^3	$\ln (\sqrt{a b^{3}})$
37337	Expand the Logarithmic Expression	natural log of m/n	$\ln (\frac{m}{n})$
37338	Expand the Logarithmic Expression	natural log of r^7s^8 seventh root of r^4s^9	$\ln (r^{7} s^{8} \sqrt[7]{r^{4} s^{9}})$
37339	Expand the Logarithmic Expression	natural log of r^8s^6 cube root of r^9s^2	$\ln (r^{8} s^{6} \sqrt[3]{r^{9} s^{2}})$
37340	Expand the Logarithmic Expression	natural log of square root of (x^2)/(y^2)	$\ln (\sqrt{\frac{x^{2}}{y^{2}}})$
37341	Expand the Logarithmic Expression	natural log of square root of x^3* fourth root of y	$\ln (\sqrt{x^{3} \cdot \sqrt[4]{y}})$
37342	Expand the Logarithmic Expression	natural log of square root of x^7y	$\ln (\sqrt{x^{7} y})$
37343	Expand the Logarithmic Expression	natural log of square root of x^8(x+5)	$\ln (\sqrt{x^{8} (x + 5)})$
37344	Expand the Logarithmic Expression	natural log of square root of x^9(x+9)	$\ln (\sqrt{x^{9} (x + 9)})$
37345	Expand the Logarithmic Expression	natural log of square root of (x-6)/x	$\ln (\sqrt{\frac{x - 6}{x}})$
37346	Expand the Logarithmic Expression	natural log of square root of (xy)/(e^7z)	$\ln (\sqrt{\frac{x y}{e^{7} z}})$
37347	Expand the Logarithmic Expression	natural log of square root of 15a^7c^7	$\ln (\sqrt{15 a^{7} c^{7}})$
37348	Expand the Logarithmic Expression	natural log of cube root of (x^2y)/z	$\ln (\sqrt[3]{\frac{x^{2} y}{z}})$
37349	Expand the Logarithmic Expression	natural log of square root of x-1	$\ln (\sqrt{x - 1})$
37350	Expand the Logarithmic Expression	natural log of square root of x-8	$\ln (\sqrt{x - 8})$
37351	Expand the Logarithmic Expression	natural log of 11 root of e	$\ln (\sqrt[11]{e})$
37352	Expand the Logarithmic Expression	natural log of 10 root of x^9(x^5+9)	$\ln (\sqrt[10]{x^{9} (x^{5} + 9)})$
37353	Expand the Logarithmic Expression	natural log of square root of 5e^3x^4	$\ln (\sqrt{5 e^{3} x^{4}})$
37354	Expand the Logarithmic Expression	natural log of square root of 6x^7y^3	$\ln (\sqrt{6 x^{7} y^{3}})$
37355	Expand the Logarithmic Expression	natural log of square root of 6	$\ln (\sqrt{6})$
37356	Expand the Logarithmic Expression	natural log of square root of x(x^2-1)	$\ln (\sqrt{x (x^{2} - 1)})$
37357	Graph	r=3sin(2)theta	$r = 3 \sin (2) θ$
37358	Expand the Logarithmic Expression	natural log of square root of (x^2)/(y^6)	$\ln (\sqrt{\frac{x^{2}}{y^{6}}})$
37359	Expand the Logarithmic Expression	natural log of square root of (x^2+4)/((x^2+1)(x^3-7)^2)	$\ln (\sqrt{\frac{x^{2} + 4}{(x^{2} + 1) {(x^{3} - 7)}^{2}}})$
37360	Expand the Logarithmic Expression	natural log of square root of (x^3y^2)/z	$\ln (\sqrt{\frac{x^{3} y^{2}}{z}})$
37361	Expand the Logarithmic Expression	natural log of square root of (x^3y^4)/(3z)	$\ln (\sqrt{\frac{x^{3} y^{4}}{3 z}})$
37362	Expand the Logarithmic Expression	natural log of square root of (x^3)/(y^2)	$\ln (\sqrt{\frac{x^{3}}{y^{2}}})$
37363	Expand the Logarithmic Expression	log of (ABC)/D	$\log (\frac{A B C}{D})$
37364	Expand the Logarithmic Expression	log of (100x^4 cube root of 5-x)/(7(x+5)^2)	$\log (\frac{100 x^{4} \sqrt[3]{5 - x}}{7 {(x + 5)}^{2}})$
37365	Expand the Logarithmic Expression	log of (7x^2 cube root of 1-x)/(8(x+1)^2)	$\log (\frac{7 x^{2} \sqrt[3]{1 - x}}{8 {(x + 1)}^{2}})$
37366	Expand the Logarithmic Expression	- log of 1.3x*10^-4	$- \log (1.3 x \cdot 10^{- 4})$
37367	Expand the Logarithmic Expression	natural log of x-8	$\ln (x - 8)$
37368	Expand the Logarithmic Expression	natural log of x/(e^(7x))	$\ln (\frac{x}{e^{7 x}})$
37369	Expand the Logarithmic Expression	natural log of x(x+6)	$\ln (x (x + 6))$
37370	Expand the Logarithmic Expression	natural log of e(x-2)	$\ln (e (x - 2))$
37371	Expand the Logarithmic Expression	natural log of x(x-7)	$\ln (x (x - 7))$
37372	Expand the Logarithmic Expression	natural log of e*91	$\ln (e) \cdot 91$
37373	Expand the Logarithmic Expression	natural log of ex	$\ln (e) x$
37374	Expand the Logarithmic Expression	natural log of e* square root of (x^6)/(e^2)	$\ln (e \cdot \sqrt{\frac{x^{6}}{e^{2}}})$
37375	Expand the Logarithmic Expression	natural log of x(x-8)	$\ln (x) (x - 8)$
37376	Expand the Logarithmic Expression	natural log of x- natural log of x	$\ln (x) - \ln (x)$
37377	Expand the Logarithmic Expression	log of (100x^3 cube root of 2-x)/(7(x+1)^2)	$\log (\frac{100 x^{3} \sqrt[3]{2 - x}}{7 {(x + 1)}^{2}})$
37378	Expand the Logarithmic Expression	log of (2x^3y)/(z^2)	$\log (\frac{2 x^{3} y}{z^{2}})$
37379	Expand the Logarithmic Expression	log of (3x)/z	$\log (\frac{3 x}{z})$
37380	Expand the Logarithmic Expression	log of (8x^2 fourth root of 4-x)/(9(x+4)^2)	$\log (\frac{8 x^{2} \sqrt[4]{4 - x}}{9 {(x + 4)}^{2}})$
37381	Expand the Logarithmic Expression	log of (ABC)/C	$\log (\frac{A B C}{C})$
37382	Expand the Logarithmic Expression	log of ((x-2)(x+2))/(v(x^2-4))	$\log (\frac{(x - 2) (x + 2)}{v (x^{2} - 4)})$
37383	Expand the Logarithmic Expression	log of ((7-x)^5)/(y^2+7)	$\log (\frac{{(7 - x)}^{5}}{y^{2} + 7})$
37384	Expand the Logarithmic Expression	log of ( square root of z^9x)/(y^4)	$\log (\frac{\sqrt{z^{9} x}}{y^{4}})$
37385	Expand the Logarithmic Expression	log of ( square root of xy^3)/(x^7)	$\log (\frac{\sqrt{x} y^{3}}{x^{7}})$
37386	Expand the Logarithmic Expression	log of ( fifth root of a^4 cube root of b)/10000	$\log (\frac{\sqrt[5]{a^{4}} \sqrt[3]{b}}{10000})$
37387	Expand the Logarithmic Expression	log of (x^2y^3)/(zw)	$\log (\frac{x^{2} y^{3}}{z w})$
37388	Expand the Logarithmic Expression	log of (x^2y^9)/(z^8)	$\log (\frac{x^{2} y^{9}}{z^{8}})$
37389	Expand the Logarithmic Expression	log of (x^4)/(y^2z^7)	$\log (\frac{x^{4}}{y^{2} z^{7}})$
37390	Expand the Logarithmic Expression	natural log of z(z-1)^9	$\ln (z) {(z - 1)}^{9}$
37391	Expand the Logarithmic Expression	natural log of z(z-1)^2	$\ln (z {(z - 1)}^{2})$
37392	Expand the Logarithmic Expression	natural log of cube root of 64m	$\ln (\sqrt[3]{64 m})$
37393	Expand the Logarithmic Expression	( natural log of x(x+1))/((x-1)^2)	$\frac{\ln (x (x + 1))}{{(x - 1)}^{2}}$
37394	Expand the Logarithmic Expression	log of 2x+3y-4z	$\log (2 x + 3 y - 4 z)$
37395	Expand the Logarithmic Expression	log of (3x^2y)(x+2y)	$\log ((3 x^{2} y) (x + 2 y))$
37396	Expand the Logarithmic Expression	log of (s square root of 7)t^2	$\log ((s \sqrt{7}) t^{2})$
37397	Expand the Logarithmic Expression	log of ((x+3)^3y^4)/(z^5)	$\log (\frac{{(x + 3)}^{3} y^{4}}{z^{5}})$
37398	Expand the Logarithmic Expression	log of ((x-7)^2 square root of x)/((5^x) natural log of x)	$\log (\frac{{(x - 7)}^{2} \sqrt{x}}{(5^{x}) \ln (x)})$
37399	Expand the Logarithmic Expression	log of ((zx)^4)/y2	$\log (\frac{{(z \cdot x)}^{4}}{y}) \cdot 2$
37400	Expand the Logarithmic Expression	log of ((z+2)^9y^4)/( square root of x)	$\log (\frac{{(z + 2)}^{9} y^{4}}{\sqrt{x}})$