Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
16301	Expand the Logarithmic Expression	log base 8 of a^6b^5	$\log_{8} (a^{6} b^{5})$
16302	Expand the Logarithmic Expression	log base 6 of seventh root of 19	$\log_{6} (\sqrt[7]{19})$
16303	Expand the Logarithmic Expression	log base 6 of (y^5)/( cube root of x)	$\log_{6} (\frac{y^{5}}{\sqrt[3]{x}})$
16304	Expand the Logarithmic Expression	log base 6 of (xy^2)/( square root of z)	$\log_{6} (\frac{x y^{2}}{\sqrt{z}})$
16305	Expand the Logarithmic Expression	log base 6 of x/11	$\log_{6} (\frac{x}{11})$
16306	Expand the Logarithmic Expression	log base 6 of 7*3	$\log_{6} (7 \cdot 3)$
16307	Expand the Logarithmic Expression	log base 6 of ab	$\log_{6} (a b)$
16308	Expand the Logarithmic Expression	log base 7 of square root of x^2+5	$\log_{7} (\sqrt{x^{2} + 5})$
16309	Expand the Logarithmic Expression	log base 3 of 33	$\log_{3} (33)$
16310	Expand the Logarithmic Expression	log base 5 of ( square root of c)/25	$\log_{5} (\frac{\sqrt{c}}{25})$
16311	Expand the Logarithmic Expression	log base 5 of (x^4)/(y^8)	$\log_{5} (\frac{x^{4}}{y^{8}})$
16312	Expand the Logarithmic Expression	log base 5 of ( cube root of x^2+1)/(x^2-1)	$\log_{5} (\frac{\sqrt[3]{x^{2} + 1}}{x^{2} - 1})$
16313	Expand the Logarithmic Expression	log base 5 of 25/( square root of x+8)	$\log_{5} (\frac{25}{\sqrt{x + 8}})$
16314	Expand the Logarithmic Expression	log base 5 of 25/( square root of x+9)	$\log_{5} (\frac{25}{\sqrt{x + 9}})$
16315	Expand the Logarithmic Expression	log base 5 of x^(2/9)	$\log_{5} (x^{\frac{2}{9}})$
16316	Expand the Logarithmic Expression	log base 5 of 225	$\log_{5} (225)$
16317	Expand the Logarithmic Expression	log base 5 of x^6	$\log_{5} (x^{6})$
16318	Expand the Logarithmic Expression	log base 5 of a^6b^-3c^4	$\log_{5} (a^{6} b^{- 3} c^{4})$
16319	Expand the Logarithmic Expression	log base 5 of fifth root of 625	$\log_{5} (\sqrt[5]{625})$
16320	Expand the Logarithmic Expression	log base 5 of 30	$\log_{5} (30)$
16321	Expand the Logarithmic Expression	log base 5 of 25*125	$\log_{5} (25 \cdot 125)$
16322	Expand the Logarithmic Expression	log base 3 of (xy^5)/(z^4)	$\log_{3} (\frac{x y^{5}}{z^{4}})$
16323	Expand the Logarithmic Expression	log base 3 of (x^12)/(x-7)	$\log_{3} (\frac{x^{12}}{x - 7})$
16324	Expand the Logarithmic Expression	log base 2 of 2x^3	$\log_{2} (2 x^{3})$
16325	Expand the Logarithmic Expression	log base 2 of 6x	$\log_{2} (6 x)$
16326	Expand the Logarithmic Expression	log base 2 of square root of y/8	$\log_{2} (\sqrt{\frac{y}{8}})$
16327	Expand the Logarithmic Expression	log base 2 of (6x^2z^3)/y	$\log_{2} (\frac{6 x^{2} z^{3}}{y})$
16328	Expand the Logarithmic Expression	log base 2 of a/(b^2)	$\log_{2} (\frac{a}{b^{2}})$
16329	Expand the Logarithmic Expression	log base 4 of xy^7z^4	$\log_{4} (x y^{7} z^{4})$
16330	Expand the Logarithmic Expression	log base 4 of x^2-64-5 log base 4 of x+8	$\log_{4} (x^{2} - 64) - 5 \log_{4} (x + 8)$
16331	Expand the Logarithmic Expression	log base 4 of x^4* square root of y	$\log_{4} (x^{4}) \cdot \sqrt{y}$
16332	Expand the Logarithmic Expression	log base 4 of cube root of 16	$\log_{4} (\sqrt[3]{16})$
16333	Expand the Logarithmic Expression	log base 4 of square root of x/9	$\log_{4} (\sqrt{\frac{x}{9}})$
16334	Expand the Logarithmic Expression	log base 4 of (x^6y^5)/(z fifth root of w^6)	$\log_{4} (\frac{x^{6} y^{5}}{z \sqrt[5]{w^{6}}})$
16335	Expand the Logarithmic Expression	log base 4 of 6^3*11^3	$\log_{4} (6^{3} \cdot 11^{3})$
16336	Expand the Logarithmic Expression	log base 4 of 13	$\log_{4} (13)$
16337	Expand the Logarithmic Expression	log base 36 of square root of 6	$\log_{36} (\sqrt{6})$
16338	Expand the Logarithmic Expression	log base 4 of (xy^4)/(z^5)	$\log_{4} (\frac{x y^{4}}{z^{5}})$
16339	Expand the Logarithmic Expression	log base 4 of 3/5	$\log_{4} (\frac{3}{5})$
16340	Expand the Logarithmic Expression	log base 3 of 6^3*9^6	$\log_{3} (6^{3} \cdot 9^{6})$
16341	Expand the Logarithmic Expression	log base 3 of 9/( square root of x)	$\log_{3} (\frac{9}{\sqrt{x}})$
16342	Expand the Logarithmic Expression	log base 3 of square root of x- log base 3 of x^3	$\log_{3} (\sqrt{x}) - \log_{3} (x^{3})$
16343	Expand the Logarithmic Expression	log base 3 of fourth root of (x^2y)/3	$\log_{3} (\sqrt[4]{\frac{x^{2} y}{3}})$
16344	Expand the Logarithmic Expression	log base 3 of 11z	$\log_{3} (11 z)$
16345	Expand the Logarithmic Expression	log base 3 of x/9	$\log_{3} (\frac{x}{9})$
16346	Expand the Logarithmic Expression	log base 3 of 7*11	$\log_{3} (7 \cdot 11)$
16347	Expand the Logarithmic Expression	log base 3 of 243x	$\log_{3} (243 x)$
16348	Simplify/Condense	6 natural log of x+1/2* natural log of x^2+8-7 natural log of x+8	$6 \ln (x) + \frac{1}{2} \cdot \ln (x^{2} + 8) - 7 \ln (x + 8)$
16349	Simplify/Condense	natural log of e^(4x)	$\ln (e^{4 x})$
16350	Simplify/Condense	log of cube root of 10	$\log (\sqrt[3]{10})$
16351	Simplify/Condense	log of 1.35*10^35	$\log (1.35 \cdot 10^{35})$
16352	Simplify/Condense	log of 6.4	$\log (6.4)$
16353	Simplify/Condense	log of 12*16	$\log (12) \cdot 16$
16354	Simplify/Condense	log of 125*5	$\log (125) \cdot 5$
16355	Simplify/Condense	2 log of 6-3 log of 2	$2 \log (6) - 3 \log (2)$
16356	Simplify/Condense	log of 6+4 log of 2	$\log (6) + 4 \log (2)$
16357	Expand the Logarithmic Expression	log base 2 of (2x)^3y^4	$\log_{2} ({(2 x)}^{3} y^{4})$
16358	Simplify/Condense	log of log of 10000^(250x)	$\log (\log (10000^{250 x}))$
16359	Expand the Logarithmic Expression	log base 9 of (x)^2	$\log_{9} ({(x)}^{2})$
16360	Expand the Logarithmic Expression	log base a of (30a)^3	$\log_{a} ({(30 a)}^{3})$
16361	Expand the Logarithmic Expression	log base 3 of (4x)^4	$\log_{3} ({(4 x)}^{4})$
16362	Expand the Logarithmic Expression	log base 5 of (u square root of t)^3	$\log_{5} ({(u \sqrt{t})}^{3})$
16363	Expand the Logarithmic Expression	log base 2 of (xy)^6	$\log_{2} ({(x y)}^{6})$
16364	Expand the Logarithmic Expression	log base 3 of (x/(y^3))^6	$\log_{3} ({(\frac{x}{y^{3}})}^{6})$
16365	Expand the Logarithmic Expression	log base 5 of (x/25)^3	$\log_{5} ({(\frac{x}{25})}^{3})$
16366	Expand the Logarithmic Expression	log base 2 of 4/( square root of x+9)	$\log_{2} (\frac{4}{\sqrt{x + 9}})$
16367	Expand the Logarithmic Expression	log base 16 of (15 square root of x)/y	$\log_{16} (\frac{15 \sqrt{x}}{y})$
16368	Expand the Logarithmic Expression	log base 2 of ( square root of g)/8	$\log_{2} (\frac{\sqrt{g}}{8})$
16369	Expand the Logarithmic Expression	log base 2 of ( square root of f)/4	$\log_{2} (\frac{\sqrt{f}}{4})$
16370	Expand the Logarithmic Expression	log of (xy^4)/(z^5)	$\log (\frac{x y^{4}}{z^{5}})$
16371	Expand the Logarithmic Expression	log of (xy)^3	$\log ({(x y)}^{3})$
16372	Expand the Logarithmic Expression	( natural log of x)/( natural log of y)	$\frac{\ln (x)}{\ln (y)}$
16373	Expand the Logarithmic Expression	natural log of (8)^2	$\ln ({(8)}^{2})$
16374	Expand the Logarithmic Expression	log of (8r)^5	$\log ({(8 r)}^{5})$
16375	Expand the Logarithmic Expression	natural log of (xyz)^2	$\ln ({(x y z)}^{2})$
16376	Expand the Logarithmic Expression	log base 0.25 of 5	$\log_{0.25} (5)$
16377	Expand the Logarithmic Expression	10^( log of 36)	$10^{\log (36)}$
16378	Expand the Logarithmic Expression	e^(4 natural log of x-2)	$e^{4 \ln (x - 2)}$
16379	Expand the Logarithmic Expression	e^(4 natural log of x-3)	$e^{4 \ln (x - 3)}$
16380	Expand the Logarithmic Expression	e^( natural log of 4a)	$e^{\ln (4 a)}$
16381	Expand the Logarithmic Expression	( natural log of 1/((ab)^4))/( natural log of bc)	$\frac{\ln (\frac{1}{{(a b)}^{4}})}{\ln (b c)}$
16382	Expand the Logarithmic Expression	natural log of ((5^2)/2)^5	$\ln ({(\frac{5^{2}}{2})}^{5})$
16383	Write in Exponential Form	2 log of x = log of 2+ log of 5x-8	$2 \log (x) = \log (2) + \log (5 x - 8)$
16384	Write in Exponential Form	2x natural log of 1/x-x=0	$2 x \ln (\frac{1}{x}) - x = 0$
16385	Write in Exponential Form	3 log base 2 of x-1=5- log base 2 of 4	$3 \log_{2} (x - 1) = 5 - \log_{2} (4)$
16386	Write in Exponential Form	-2 log base 4 of x = log base 4 of 9	$- 2 \log_{4} (x) = \log_{4} (9)$
16387	Write in Exponential Form	2 log base 4 of x=3	$2 \log_{4} (x) = 3$
16388	Write in Exponential Form	-2 log base 5 of 7x=2	$- 2 \log_{5} (7 x) = 2$
16389	Write in Exponential Form	1+ log of 4x-1 = log of 8x+1	$1 + \log (4 x - 1) = \log (8 x + 1)$
16390	Write in Exponential Form	log base x of 1/32=5	$\log_{x} (\frac{1}{32}) = 5$
16391	Write in Exponential Form	x^(1+ log base x of 16)=4x^2	$x^{1 + \log_{x} (16)} = 4 x^{2}$
16392	Write in Exponential Form	log base x of 625=4	$\log_{x} (625) = 4$
16393	Write in Exponential Form	log base 9 of y=2	$\log_{9} (y) = 2$
16394	Write in Exponential Form	log base 9 of x^2-8x=1	$\log_{9} (x^{2} - 8 x) = 1$
16395	Write in Exponential Form	log base 9 of 27=3* log base 9 of x	$\log_{9} (27) = 3 \cdot \log_{9} (x)$
16396	Write in Exponential Form	log base 4 of -9b-7=-5	$\log_{4} (- 9 b) - 7 = - 5$
16397	Write in Exponential Form	log base 5 of 4x-5=3	$\log_{5} (4 x - 5) = 3$
16398	Write in Exponential Form	log base 49 of x=1/2	$\log_{49} (x) = \frac{1}{2}$
16399	Write in Exponential Form	log base 4 of 112=x	$\log_{4} (112) = x$
16400	Expand the Logarithmic Expression	log of 10000x^3y^5	$\log (10000 x^{3} y^{5})$