Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
38601	Expand the Logarithmic Expression	( natural log of 0.80)/( natural log of -0.15)	$\frac{\ln (0.8)}{\ln (- 0.15)}$
38602	Expand the Logarithmic Expression	natural log of ((x^2-x-6)/((x+6)^2))^(1/3)	$\ln ({(\frac{x^{2} - x - 6}{{(x + 6)}^{2}})}^{\frac{1}{3}})$
38603	Expand the Logarithmic Expression	natural log of ((2x+3)/(x^2-3x+2))^2	$\ln ({(\frac{2 x + 3}{x^{2} - 3 x + 2})}^{2})$
38604	Expand the Logarithmic Expression	natural log of (((x+6)(x-2))/((x-8)^2))^(3/4)	$\ln ({(\frac{(x + 6) (x - 2)}{{(x - 8)}^{2}})}^{\frac{3}{4}})$
38605	Expand the Logarithmic Expression	( natural log of 1/(a^4)*1/(b^4))/( natural log of bc)	$\frac{\ln (\frac{1}{a^{4}} \cdot \frac{1}{b^{4}})}{\ln (b c)}$
38606	Expand the Logarithmic Expression	10000^(3 log of x^3)	$10000^{3 \log (x^{3})}$
38607	Expand the Logarithmic Expression	2^( log base 2 of 5x-8)	$2^{\log_{2} (5 x - 8)}$
38608	Expand the Logarithmic Expression	2^( log base 8 of 125)	$2^{\log_{8} (125)}$
38609	Expand the Logarithmic Expression	2^( log base 8 of 169)	$2^{\log_{8} (169)}$
38610	Expand the Logarithmic Expression	(24 natural log of 2)/(4 natural log of 2+5 natural log of 3)	$\frac{24 \ln (2)}{4 \ln (2) + 5 \ln (3)}$
38611	Expand the Logarithmic Expression	(2- natural log of 1306)/3	$\frac{2 - \ln (1306)}{3}$
38612	Expand the Logarithmic Expression	2 log of (3)^x	$2 \log ({(3)}^{x})$
38613	Expand the Logarithmic Expression	3/8* log base a of x^16y^8+9 log base a of x^(4/9)-12 log base a of y	$\frac{3}{8} \cdot \log_{a} (x^{16} y^{8}) + 9 \log_{a} (x^{\frac{4}{9}}) - 12 \log_{a} (y)$
38614	Expand the Logarithmic Expression	3/( natural log of 4)+2/(( natural log of 2)^3)+(2( natural log of 2-1)^2)/(( natural log of 2)^3)+1/5	$\frac{3}{\ln (4)} + \frac{2}{\ln^{3} (2)} + \frac{2 {(\ln (2) - 1)}^{2}}{\ln^{3} (2)} + \frac{1}{5}$
38615	Expand the Logarithmic Expression	3^( log base 3 of 10)	$3^{\log_{3} (10)}$
38616	Expand the Logarithmic Expression	3^( log base 3 of 23)	$3^{\log_{3} (23)}$
38617	Expand the Logarithmic Expression	3^( log base 3 of 6.47)	$3^{\log_{3} (6.47)}$
38618	Expand the Logarithmic Expression	3^(5 log base 3 of 2+2)	$3^{5 \log_{3} (2 + 2)}$
38619	Expand the Logarithmic Expression	4^( log base 4 of x^4-7 log base 4 of y)	$4^{\log_{4} (x^{4}) - 7 \log_{4} (y)}$
38620	Expand the Logarithmic Expression	(4 log of 5)/( log of 4)	$\frac{4 \log (5)}{\log (4)}$
38621	Expand the Logarithmic Expression	5/(9 log of 10)	$\frac{5}{9 \log (10)}$
38622	Expand the Logarithmic Expression	5^( log of 5^3)	$5^{\log (5^{3})}$
38623	Expand the Logarithmic Expression	6^( log base 6 of 36)	$6^{\log_{6} (36)}$
38624	Expand the Logarithmic Expression	6^(2 log base 6 of 5)	$6^{2 \log_{6} (5)}$
38625	Expand the Logarithmic Expression	6^(35 log base 6 of x)	$6^{35 \log_{6} (x)}$
38626	Expand the Logarithmic Expression	7^( log base 7 of square root of x)	$7^{\log_{7} (\sqrt{x})}$
38627	Expand the Logarithmic Expression	-8/9* log base 5 of 5m^2+1/2* log base 5 of 25m^2	$- \frac{8}{9} \cdot \log_{5} (5 m^{2}) + \frac{1}{2} \cdot \log_{5} (25 m^{2})$
38628	Expand the Logarithmic Expression	(9 natural log of 145-12)/(4-4 natural log of 145)	$\frac{9 \ln (145) - 12}{4 - 4 \ln (145)}$
38629	Expand the Logarithmic Expression	log base p of (P)^5	$\log_{p} ({(P)}^{5})$
38630	Expand the Logarithmic Expression	( log base u of v^9)/( log base u of t^4)	$\frac{\log_{u} (v^{9})}{\log_{u} (t^{4})}$
38631	Expand the Logarithmic Expression	1/(1+ log base c of ab)+1/(1+ log base a of bc)+1/(1+ log base b of ca)	$\frac{1}{1 + \log_{c} (a b)} + \frac{1}{1 + \log_{a} (b c)} + \frac{1}{1 + \log_{b} (c a)}$
38632	Expand the Logarithmic Expression	1/2*( log base 2 of a+ log base 2 of b)	$\frac{1}{2} \cdot (\log_{2} (a) + \log_{2} (b))$
38633	Expand the Logarithmic Expression	1/3*(2 log of z-3 log of x+5 log of y)	$\frac{1}{3} \cdot (2 \log (z) - 3 \log (x) + 5 \log (y))$
38634	Expand the Logarithmic Expression	1/3* log base 2 of x-6-4 log base 2 of z+2 log base 3 of y	$\frac{1}{3} \cdot \log_{2} (x - 6) - 4 \log_{2} (z) + 2 \log_{3} (y)$
38635	Expand the Logarithmic Expression	1/4( natural log of x+3 natural log of x-1)-1/2 natural log of x+2	$\frac{1}{4} \cdot (\ln (x + 3) \ln (x - 1)) - \frac{1}{2} \cdot \ln (x + 2)$
38636	Expand the Logarithmic Expression	1/5* log base 3 of (a^6b)/9	$\frac{1}{5} \cdot \log_{3} (\frac{a^{6} b}{9})$
38637	Expand the Logarithmic Expression	1/7*( log base 19 of 6-2 log base 19 of n)- log base 19 of m	$\frac{1}{7} \cdot (\log_{19} (6 - 2) \log_{19} (n)) - \log_{19} (m)$
38638	Expand the Logarithmic Expression	1/8*(5 natural log of x+4- natural log of x- natural log of x^2-25)	$\frac{1}{8} \cdot (5 \ln (x + 4) - \ln (x) - \ln (x^{2} - 25))$
38639	Expand the Logarithmic Expression	10^( log of square root of z)	$10^{\log (\sqrt{z})}$
38640	Expand the Logarithmic Expression	10^( log of 0.82)	$10^{\log (0.82)}$
38641	Expand the Logarithmic Expression	e^(6-2 natural log of x+ natural log of y)	$e^{6 - 2 \ln (x) + \ln (y)}$
38642	Expand the Logarithmic Expression	e^(a natural log of x)	$e^{a \ln (x)}$
38643	Expand the Logarithmic Expression	e^( natural log of 1/((1-x)(1+x)))	$e^{\ln (\frac{1}{(1 - x) (1 + x)})}$
38644	Expand the Logarithmic Expression	e^( natural log of 22)	$e^{\ln (22)}$
38645	Expand the Logarithmic Expression	e^( natural log of 24)	$e^{\ln (24)}$
38646	Expand the Logarithmic Expression	10^( log of v)	$10^{\log (v)}$
38647	Expand the Logarithmic Expression	1000^(3 log of x^3)	$1000^{3 \log (x^{3})}$
38648	Expand the Logarithmic Expression	( log base b of square root of xy^6)/(z^6)	$\frac{\log_{b} (\sqrt{x y^{6}})}{z^{6}}$
38649	Expand the Logarithmic Expression	( log base b of cube root of xy^4)/(z^5)	$\frac{\log_{b} (\sqrt[3]{x y^{4}})}{z^{5}}$
38650	Expand the Logarithmic Expression	log base b of (4mn)^5	$\log_{b} ({(4 m n)}^{5})$
38651	Expand the Logarithmic Expression	10^( log of 45)	$10^{\log (45)}$
38652	Expand the Logarithmic Expression	10^( log of 4x)	$10^{\log (4 x)}$
38653	Expand the Logarithmic Expression	log base 0.25 of 9	$\log_{0.25} (9)$
38654	Expand the Logarithmic Expression	log base 0.33 of 729	$\log_{0.33} (729)$
38655	Expand the Logarithmic Expression	log base 0.333 of x	$\log_{0.333} (x)$
38656	Expand the Logarithmic Expression	log base 0.4 of 125/8	$\log_{0.4} (\frac{125}{8})$
38657	Expand the Logarithmic Expression	log base 0.5 of -3	$\log_{0.5} (- 3)$
38658	Expand the Logarithmic Expression	log base 0.5 of 4	$\log_{0.5} (4)$
38659	Expand the Logarithmic Expression	log base 0.5 of 512	$\log_{0.5} (512)$
38660	Expand the Logarithmic Expression	log base 1/3 of 27	$\log_{\frac{1}{3}} (27)$
38661	Expand the Logarithmic Expression	log base 1/5 of 625	$\log_{\frac{1}{5}} (625)$
38662	Expand the Logarithmic Expression	log base 1/7 of cube root of 7	$\log_{\frac{1}{7}} (\sqrt[3]{7})$
38663	Expand the Logarithmic Expression	log base square root of 3*3 of 8	$\log_{\sqrt{3} \cdot 3} (8)$
38664	Expand the Logarithmic Expression	log base 0.1 of 21.8	$\log_{0.1} (21.8)$
38665	Expand the Logarithmic Expression	log base 0.16 of 4	$\log_{0.16} (4)$
38666	Expand the Logarithmic Expression	log base 0.2 of 1/5	$\log_{0.2} (\frac{1}{5})$
38667	Expand the Logarithmic Expression	log base 0.2 of 2	$\log_{0.2} (2)$
38668	Expand the Logarithmic Expression	log base 0.2 of 4	$\log_{0.2} (4)$
38669	Expand the Logarithmic Expression	log base 0.25 of 1024	$\log_{0.25} (1024)$
38670	Expand the Logarithmic Expression	log base 0.32 of 4	$\log_{0.32} (4)$
38671	Expand the Logarithmic Expression	log base 0.5 of 0	$\log_{0.5} (0)$
38672	Expand the Logarithmic Expression	log base 0.5 of 6	$\log_{0.5} (6)$
38673	Expand the Logarithmic Expression	log base 0.6 of 2 7/9	$\log_{0.6} (2 \frac{7}{9})$
38674	Expand the Logarithmic Expression	log base 0.7 of 15	$\log_{0.7} (15)$
38675	Expand the Logarithmic Expression	log base 1.02 of 6	$\log_{1.02} (6)$
38676	Expand the Logarithmic Expression	log base 1.051 of 2	$\log_{1.051} (2)$
38677	Expand the Logarithmic Expression	log base 1.099 of square root of 1.099^3	$\log_{1.099} (\sqrt{{1.099}^{3}})$
38678	Expand the Logarithmic Expression	log base 1 of 0.22	$\log_{1} (0.22)$
38679	Expand the Logarithmic Expression	log base 1 of 12	$\log_{1} (12)$
38680	Expand the Logarithmic Expression	log base 1 of x	$\log_{1} (x)$
38681	Expand the Logarithmic Expression	log of (10^x)/(x(x^2+1)(x^4+2))	$\log (\frac{10^{x}}{x (x^{2} + 1) (x^{4} + 2)})$
38682	Expand the Logarithmic Expression	log of ( square root of xy)/19	$\log (\frac{\sqrt{x y}}{19})$
38683	Expand the Logarithmic Expression	natural log of (xyz)^6	$\ln ({(x y z)}^{6})$
38684	Expand the Logarithmic Expression	natural log of (xz)^9	$\ln ({(x z)}^{9})$
38685	Expand the Logarithmic Expression	log of ((3^3)/7)^4	$\log ({(\frac{3^{3}}{7})}^{4})$
38686	Expand the Logarithmic Expression	log of ((n^5 square root of m)/k)^5	$\log ({(\frac{n^{5} \sqrt{m}}{k})}^{5})$
38687	Expand the Logarithmic Expression	log of ((x^3)/y)^6	$\log ({(\frac{x^{3}}{y})}^{6})$
38688	Expand the Logarithmic Expression	( log of 1/2)/9	$\frac{\log (\frac{1}{2})}{9}$
38689	Expand the Logarithmic Expression	log of (1/5)^5	$\log ({(\frac{1}{5})}^{5})$
38690	Expand the Logarithmic Expression	( log of 1/8)/( log of square root of 2)	$\frac{\log (\frac{1}{8})}{\log (\sqrt{2})}$
38691	Expand the Logarithmic Expression	( log of 19871.19/19000)/(4* log of 1.0075)	$\frac{\log (\frac{19871.19}{19000})}{4 \cdot \log (1.0075)}$
38692	Expand the Logarithmic Expression	( log of 57)/(56 log of 7csc(4.9/( square root of 78)))	$\frac{\log (57)}{56 \log (7 \csc (\frac{4.9}{\sqrt{78}}))}$
38693	Expand the Logarithmic Expression	( log of 625)/( log of 125)	$\frac{\log (625)}{\log (125)}$
38694	Expand the Logarithmic Expression	( log of 8)/( log of 6)	$\frac{\log (8)}{\log (6)}$
38695	Expand the Logarithmic Expression	natural log of (a)^(3b)	$\ln ({(a)}^{3 b})$
38696	Expand the Logarithmic Expression	natural log of (a)^b	$\ln ({(a)}^{b})$
38697	Expand the Logarithmic Expression	natural log of (e)^(14x)	$\ln ({(e)}^{14 x})$
38698	Expand the Logarithmic Expression	natural log of (e)^3- natural log of (e)^7	$\ln ({(e)}^{3}) - \ln ({(e)}^{7})$
38699	Expand the Logarithmic Expression	natural log of (e)^(6x)	$\ln ({(e)}^{6 x})$
38700	Expand the Logarithmic Expression	natural log of (e)^-8	$\ln ({(e)}^{- 8})$