Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
22401	Simplify/Condense	natural log of x*e^(4x)(x)	$\ln (x \cdot e^{4 x}) (x)$
22402	Simplify/Condense	natural log of x cube root of 6-x	$\ln (x \sqrt[3]{6 - x})$
22403	Simplify/Condense	natural log of x+1/2 natural log of x-1-1/3* natural log of x+7-5 natural log of 2x+5	$\ln (x + \frac{1}{2}) \ln (x - 1) - \frac{1}{3} \cdot \ln (x + 7) - 5 \ln (2 x + 5)$
22404	Simplify/Condense	natural log of x+2+ natural log of x-2- natural log of x^2-4	$\ln (x + 2) + \ln (x - 2) - \ln (x^{2} - 4)$
22405	Simplify/Condense	natural log of x-3(2 natural log of x-5- natural log of x+5)	$\ln (x - 3) (2 \ln (x - 5) - \ln (x + 5))$
22406	Simplify/Condense	natural log of x-3( natural log of x-7+ natural log of x+7)	$\ln (x - 3) (\ln (x - 7) + \ln (x + 7))$
22407	Simplify/Condense	natural log of x-7( natural log of x-3+ natural log of x+3)	$\ln (x - 7) (\ln (x - 3) + \ln (x + 3))$
22408	Simplify/Condense	natural log of x-8- natural log of x+1	$\ln (x - 8) - \ln (x + 1)$
22409	Simplify/Condense	natural log of xy+2 natural log of yz^2- natural log of xz	$\ln (x y) + 2 \ln (y z^{2}) - \ln (x z)$
22410	Simplify/Condense	natural log of xyz	$\ln (x y z)$
22411	Simplify/Condense	natural log of z-3+2 natural log of z+3	$\ln (z - 3) + 2 \ln (z + 3)$
22412	Simplify/Condense	natural log of a+ natural log of 2y-2 natural log of z	$\ln (a) + \ln (2 y) - 2 \ln (z)$
22413	Simplify/Condense	natural log of x-2 natural log of x^2+1+1/2* natural log of 3-4x	$\ln (x) - 2 \ln (x^{2} + 1) + \frac{1}{2} \cdot \ln (3 - 4 x)$
22414	Simplify/Condense	natural log of x-4( natural log of x+2+ natural log of x-2)	$\ln (x) - 4 (\ln (x + 2) + \ln (x - 2))$
22415	Simplify/Condense	natural log of x-4 natural log of x^3-4+1/2* natural log of 4+x^2	$\ln (x) - 4 \ln (x^{3} - 4) + \frac{1}{2} \cdot \ln (4 + x^{2})$
22416	Simplify/Condense	natural log of x+2 natural log of x+2- natural log of x^(2-1)	$\ln (x) + 2 \ln (x + 2) - \ln (x^{2 - 1})$
22417	Simplify/Condense	natural log of a+b+3 natural log of a-b-5 natural log of c	$\ln (a + b) + 3 \ln (a - b) - 5 \ln (c)$
22418	Simplify/Condense	natural log of a+b+ natural log of a-b-21 natural log of c	$\ln (a + b) + \ln (a - b) - 21 \ln (c)$
22419	Simplify/Condense	natural log of a+b+ natural log of a-b-7 natural log of c	$\ln (a + b) + \ln (a - b) - 7 \ln (c)$
22420	Simplify/Condense	natural log of a+b+ natural log of a-b-9 natural log of c	$\ln (a + b) + \ln (a - b) - 9 \ln (c)$
22421	Simplify/Condense	natural log of csc(x)+ natural log of tan(x)	$\ln (\csc (x)) + \ln (\tan (x))$
22422	Simplify/Condense	natural log of e(x+5)	$\ln (e (x + 5))$
22423	Simplify/Condense	natural log of e(x-9)	$\ln (e (x - 9))$
22424	Simplify/Condense	natural log of natural log of e^(e^3)	$\ln (\ln (e^{e^{3}}))$
22425	Simplify/Condense	natural log of natural log of natural log of x	$\ln (\ln (\ln (x)))$
22426	Simplify/Condense	natural log of o+ natural log of n- natural log of m-1	$\ln (o) + \ln (n) - \ln (m) - 1$
22427	Simplify/Condense	natural log of sin(x)+ natural log of sec(x)	$\ln (\sin (x)) + \ln (\sec (x))$
22428	Simplify/Condense	natural log of sin(x)- natural log of cos(x)	$\ln (\sin (x)) - \ln (\cos (x))$
22429	Find the Exact Value	2cos(15)cos(75)	$2 \cos (15) \cos (75)$
22430	Simplify/Condense	natural log of x-( natural log of x+1+ natural log of x-1)	$\ln (x) - (\ln (x + 1) + \ln (x - 1))$
22431	Simplify/Condense	log of 4^25	$\log (4^{25})$
22432	Simplify/Condense	log of 5/2+ log of 200000/5	$\log (\frac{5}{2}) + \log (\frac{200000}{5})$
22433	Simplify/Condense	log of 5^2+ log of 3- log of 7	$\log (5^{2}) + \log (3) - \log (7)$
22434	Simplify/Condense	log of (6x^5)/y	$\log (\frac{6 x^{5}}{y})$
22435	Simplify/Condense	log of (x^4(y+1)^9)/( square root of z)	$\log (\frac{x^{4} {(y + 1)}^{9}}{\sqrt{z}})$
22436	Simplify/Condense	log of (0(0+4))/((x+8)^2)	$\log (\frac{0 (0 + 4)}{{(x + 8)}^{2}})$
22437	Simplify/Condense	log of 1/(11 root of 11)	$\log (\frac{1}{\sqrt[11]{11}})$
22438	Simplify/Condense	log of 1/(x^5)-13 log of x	$\log (\frac{1}{x^{5}}) - 13 \log (x)$
22439	Simplify/Condense	log of 1/(x^8)-12 log of x	$\log (\frac{1}{x^{8}}) - 12 \log (x)$
22440	Simplify/Condense	log of 1/2*128	$\log (\frac{1}{2}) \cdot 128$
22441	Simplify/Condense	log of 1/2*5	$\log (\frac{1}{2}) \cdot 5$
22442	Simplify/Condense	log of 1/x+4 log of x	$\log (\frac{1}{x}) + 4 \log (x)$
22443	Simplify/Condense	log of 10^1000000	$\log (10^{1000000})$
22444	Simplify/Condense	log of 10^5x^3	$\log (10^{5} x^{3})$
22445	Simplify/Condense	log of 1000000^x	$\log (1000000^{x})$
22446	Simplify/Condense	log of (10A)/(B^2)	$\log (\frac{10 A}{B^{2}})$
22447	Simplify/Condense	log of 14/3+ log of 11/5+ log of 22/15	$\log (\frac{14}{3}) + \log (\frac{11}{5}) + \log (\frac{22}{15})$
22448	Simplify/Condense	log of 15/35* log of 189	$\log (\frac{15}{35}) \cdot \log (189)$
22449	Simplify/Condense	log of 2^16	$\log (2^{16})$
22450	Simplify/Condense	log of 70000000/(70000000(0))	$\log (\frac{70000000}{70000000 (0)})$
22451	Simplify/Condense	natural log of 17-2 natural log of x+3 natural log of y	$\ln (17) - 2 \ln (x) + 3 \ln (y)$
22452	Simplify/Condense	log of cos(x)^2	$\log (\cos^{2} (x))$
22453	Simplify/Condense	log of square root of (x^2+7)/((x^4+8)(x^2-16)^5)	$\log (\sqrt{\frac{x^{2} + 7}{(x^{4} + 8) {(x^{2} - 16)}^{5}}})$
22454	Simplify/Condense	log of square root of 5*25	$\log (\sqrt{5}) \cdot 25$
22455	Simplify/Condense	log of square root of x+ log of x^510- log of x	$\log (\sqrt{x}) + \log (x^{510}) - \log (x)$
22456	Simplify/Condense	log of cube root of (3-v)/(2v)	$\log (\sqrt[3]{\frac{3 - v}{2 v}})$
22457	Simplify/Condense	log of fifth root of (x^2)/(y^3z^5)	$\log (\sqrt[5]{\frac{x^{2}}{y^{3} z^{5}}})$
22458	Simplify/Condense	log of x^13y^12 square root of 10	$\log (x^{13} y^{12} \sqrt{10})$
22459	Simplify/Condense	5 log base 4 of x+6 log base 4 of y-1/3* log base 4 of 7z	$5 \log_{4} (x) + 6 \log_{4} (y) - \frac{1}{3} \cdot \log_{4} (7 z)$
22460	Simplify/Condense	5 log base 5 of 10	$5 \log_{5} (10)$
22461	Simplify/Condense	5 log base 5 of 3+ log base 5 of 7	$5 \log_{5} (3) + \log_{5} (7)$
22462	Simplify/Condense	5 log base 5 of 3x+5+2 log base 5 of 2x+3	$5 \log_{5} (3 x + 5) + 2 \log_{5} (2 x + 3)$
22463	Simplify/Condense	5 log base 5 of 6+ log base 5 of 7	$5 \log_{5} (6) + \log_{5} (7)$
22464	Simplify/Condense	5 log base 5 of 7-4 log base 3 of fourth root of 3	$5 \log_{5} (7) - 4 \log_{3} (\sqrt[4]{3})$
22465	Simplify/Condense	5 log base 6 of 5x+1+1/5* log base 6 of x+5	$5 \log_{6} (5 x + 1) + \frac{1}{5} \cdot \log_{6} (x + 5)$
22466	Simplify/Condense	5 log base 6 of w+( log base 6 of u)/3	$5 \log_{6} (w) + \frac{\log_{6} (u)}{3}$
22467	Simplify/Condense	5 log base 6 of x+7 log base 6 of y-6 log base 6 of z	$5 \log_{6} (x) + 7 \log_{6} (y) - 6 \log_{6} (z)$
22468	Simplify/Condense	5 log base 6 of x-20 log base 6 of y	$5 \log_{6} (x) - 20 \log_{6} (y)$
22469	Simplify/Condense	5 log base 7 of 11- log base 7 of 8	$5 \log_{7} (11) - \log_{7} (8)$
22470	Simplify/Condense	5 log base 7 of 2x-1/3* log base 7 of 5x+1	$5 \log_{7} (2 x) - \frac{1}{3} \cdot \log_{7} (5 x + 1)$
22471	Simplify/Condense	5 log base 7 of p+9 log base 7 of p	$5 \log_{7} (p) + 9 \log_{7} (p)$
22472	Simplify/Condense	5 log base 7 of x- log base 7 of 8	$5 \log_{7} (x) - \log_{7} (8)$
22473	Simplify/Condense	-5 log base 8 of 2	$- 5 \log_{8} (2)$
22474	Simplify/Condense	5 log base 8 of x+9 log base 8 of y-7 log base 8 of z	$5 \log_{8} (x) + 9 \log_{8} (y) - 7 \log_{8} (z)$
22475	Simplify/Condense	5 log base 9 of x-2 log base 9 of y	$5 \log_{9} (x) - 2 \log_{9} (y)$
22476	Simplify/Condense	5 log base a of z+7+ log base a of 2z+9	$5 \log_{a} (z + 7) + \log_{a} (2 z + 9)$
22477	Simplify/Condense	5 log base b of 2+2 log base b of x- log base b of y	$5 \log_{b} (2) + 2 \log_{b} (x) - \log_{b} (y)$
22478	Simplify/Condense	4 natural log of x+2 natural log of y-3 natural log of z	$4 \ln (x + 2) \ln (y - 3) \ln (z)$
22479	Simplify/Condense	4 natural log of x+3-1/5* natural log of 4x+7	$4 \ln (x + 3) - \frac{1}{5} \cdot \ln (4 x + 7)$
22480	Simplify/Condense	4 natural log of x+3+7 natural log of x-3-5 natural log of x	$4 \ln (x + 3) + 7 \ln (x - 3) - 5 \ln (x)$
22481	Simplify/Condense	4 natural log of x+3+ natural log of 5x+2-1/2* natural log of x^3+3+4 natural log of x-3-4 natural log of x+5	$4 \ln (x + 3) + \ln (5 x + 2) - \frac{1}{2} \cdot \ln (x^{3} + 3) + 4 \ln (x - 3) - 4 \ln (x + 5)$
22482	Simplify/Condense	4 natural log of x+3-8 natural log of x	$4 \ln (x + 3) - 8 \ln (x)$
22483	Simplify/Condense	4 log of 8*3-4 log of (8)^2	$4 \log (8) \cdot 3 - 4 \log ({(8)}^{2})$
22484	Simplify/Condense	4 log of 8x^5-1/6* log of 8x+11	$4 \log (8 x^{5}) - \frac{1}{6} \cdot \log (8 x + 11)$
22485	Simplify/Condense	4 log of a+ log of b-3 log of c	$4 \log (a) + \log (b) - 3 \log (c)$
22486	Simplify/Condense	4 log of a-3 log of b+4 log of c-7 log of d	$4 \log (a) - 3 \log (b) + 4 \log (c) - 7 \log (d)$
22487	Simplify/Condense	4 log of c-2 log of d-3 log of f	$4 \log (c) - 2 \log (d) - 3 \log (f)$
22488	Simplify/Condense	4 log of u	$4 \log (u)$
22489	Simplify/Condense	4 log of x-1/3*(x^2+1)+2 log of x-1	$4 \log (x) - \frac{1}{3} \cdot (x^{2} + 1) + 2 \log (x - 1)$
22490	Simplify/Condense	4 log of x-1/3* log of x^2+1+2 log of x-1	$4 \log (x) - \frac{1}{3} \cdot \log (x^{2} + 1) + 2 \log (x - 1)$
22491	Simplify/Condense	5 log base b of x-4 log base 6 of y+2 log base b of z	$5 \log_{b} (x - 4) \log_{6} (y + 2) \log_{b} (z)$
22492	Simplify/Condense	5 natural log of e^2+ log of 1000	$5 \ln (e^{2}) + \log (1000)$
22493	Simplify/Condense	5 log base x of x- log base x of y	$5 \log_{x} (x) - \log_{x} (y)$
22494	Simplify/Condense	5+9 natural log of x-2	$5 + 9 \ln (x) - 2$
22495	Simplify/Condense	56 log base 7 of seventh root of x+ log base 7 of 56x^4- log base 7 of 56	$56 \log_{7} (\sqrt[7]{x}) + \log_{7} (56 x^{4}) - \log_{7} (56)$
22496	Simplify/Condense	5 natural log of e^4	$5 \ln (e^{4})$
22497	Simplify/Condense	5 natural log of e^5- natural log of e^4	$5 \ln (e^{5}) - \ln (e^{4})$
22498	Simplify/Condense	5 natural log of x^2-8 natural log of square root of x	$5 \ln (x^{2}) - 8 \ln (\sqrt{x})$
22499	Simplify/Condense	5 natural log of 1x-4 natural log of y	$5 \ln (1) x - 4 \ln (y)$
22500	Simplify/Condense	5 natural log of 2+3 natural log of 4	$5 \ln (2) + 3 \ln (4)$