Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
22201	Simplify/Condense	natural log of x^2- natural log of xy	$\ln (x^{2}) - \ln (x y)$
22202	Simplify/Condense	natural log of x^2e^(2x)	$\ln (x^{2} e^{2 x})$
22203	Simplify/Condense	2 log of 3a-4 log of 3b^2	$2 \log (3 a) - 4 \log (3 b^{2})$
22204	Simplify/Condense	natural log of x^2 square root of 1-x	$\ln (x^{2} \sqrt{1 - x})$
22205	Simplify/Condense	natural log of x^2+15x+50- natural log of x+10	$\ln (x^{2} + 15 x + 50) - \ln (x + 10)$
22206	Simplify/Condense	natural log of x^2-1- natural log of x-1	$\ln (x^{2} - 1) - \ln (x - 1)$
22207	Simplify/Condense	natural log of x^2-25- natural log of x+5	$\ln (x^{2} - 25) - \ln (x + 5)$
22208	Simplify/Condense	natural log of x^2-4x+4- natural log of x-2 natural log of 8	$\ln (x^{2} - 4 x + 4) - \ln (x - 2) \ln (8)$
22209	Simplify/Condense	natural log of x^2-9-2 natural log of x-3	$\ln (x^{2} - 9) - 2 \ln (x - 3)$
22210	Simplify/Condense	natural log of 36	$\ln (36)$
22211	Simplify/Condense	natural log of 3e- natural log of 3	$\ln (3 e) - \ln (3)$
22212	Simplify/Condense	natural log of 3x+5	$\ln (3 x) + 5$
22213	Simplify/Condense	natural log of 3x-3 natural log of x+ natural log of 3y	$\ln (3 x) - 3 \ln (x) + \ln (3 y)$
22214	Simplify/Condense	natural log of 3x+2+ natural log of x+4	$\ln (3 x + 2) + \ln (x + 4)$
22215	Simplify/Condense	natural log of 3y+1- natural log of 3y^2-5y-2	$\ln (3 y + 1) - \ln (3 y^{2} - 5 y - 2)$
22216	Simplify/Condense	natural log of 3+1/2* natural log of x+3-5 natural log of 1+ square root of x	$\ln (3) + \frac{1}{2} \cdot \ln (x + 3) - 5 \ln (1 + \sqrt{x})$
22217	Simplify/Condense	natural log of 2x+3( natural log of x- natural log of y)	$\ln (2 x) + 3 (\ln (x) - \ln (y))$
22218	Simplify/Condense	natural log of 2x+3 natural log of y- natural log of x^(2-1)	$\ln (2 x) + 3 \ln (y) - \ln (x^{2 - 1})$
22219	Simplify/Condense	natural log of 2x-1+3 natural log of x-1/2* natural log of x^2+2 natural log of x-1	$\ln (2 x - 1) + 3 \ln (x - \frac{1}{2} \cdot \ln (x^{2})) + 2 \ln (x - 1)$
22220	Simplify/Condense	natural log of 2+ natural log of x+6 natural log of y- natural log of z-7	$\ln (2) + \ln (x) + 6 \ln (y) - \ln (z - 7)$
22221	Simplify/Condense	natural log of 2- natural log of y+1/2* natural log of x+y-1/3* natural log of 27	$\ln (2) - \ln (y) + \frac{1}{2} \cdot \ln (x + y) - \frac{1}{3} \cdot \ln (27)$
22222	Simplify/Condense	natural log of 2e^5	$\ln (2 e^{5})$
22223	Simplify/Condense	natural log of 200	$\ln (200)$
22224	Simplify/Condense	natural log of 24	$\ln (24)$
22225	Simplify/Condense	natural log of 243	$\ln (243)$
22226	Simplify/Condense	natural log of 25-2 natural log of 5	$\ln (25) - 2 \ln (5)$
22227	Simplify/Condense	natural log of 77+ natural log of 72	$\ln (77) + \ln (72)$
22228	Simplify/Condense	natural log of 7x	$\ln (7 x)$
22229	Simplify/Condense	natural log of 8+4 natural log of x-5 natural log of y	$\ln (8) + 4 \ln (x) - 5 \ln (y)$
22230	Simplify/Condense	natural log of 8+4 natural log of x- natural log of 3	$\ln (8) + 4 \ln (x) - \ln (3)$
22231	Simplify/Condense	natural log of 8x	$\ln (8 x)$
22232	Simplify/Condense	natural log of a+1/5* natural log of b	$\ln (a) + \frac{1}{5} \cdot \ln (b)$
22233	Simplify/Condense	natural log of a+b+2 natural log of a-b-( natural log of c)/( natural log of 5)	$\ln (a + b) + 2 \ln (a - b) - \frac{\ln (c)}{\ln (5)}$
22234	Simplify/Condense	natural log of 6-(3 natural log of x+2 natural log of 3)	$\ln (6) - (3 \ln (x) + 2 \ln (3))$
22235	Simplify/Condense	natural log of 6+5 natural log of x+4 natural log of x^2+6	$\ln (6) + 5 \ln (x) + 4 \ln (x^{2} + 6)$
22236	Simplify/Condense	natural log of 6+5 natural log of x+9 natural log of x^2+9	$\ln (6) + 5 \ln (x) + 9 \ln (x^{2} + 9)$
22237	Simplify/Condense	natural log of 6+ natural log of x- natural log of 2	$\ln (6) + \ln (x) - \ln (2)$
22238	Simplify/Condense	natural log of 5 natural log of 2 natural log of 3	$\ln (5) \ln (2) \ln (3)$
22239	Simplify/Condense	natural log of 3-2 natural log of 4+2 natural log of 2	$\ln (3) - 2 \ln (4) + 2 \ln (2)$
22240	Simplify/Condense	natural log of 3.4	$\ln (3.4)$
22241	Simplify/Condense	natural log of 3e^(2x+1)	$\ln (3 e^{2 x + 1})$
22242	Simplify/Condense	natural log of 3+x+ natural log of 2x-1-2 natural log of x	$\ln (3 + x) + \ln (2 x - 1) - 2 \ln (x)$
22243	Simplify/Condense	natural log of 34+ natural log of 46	$\ln (34) + \ln (46)$
22244	Simplify/Condense	natural log of square root of 20	$\ln (\sqrt{20})$
22245	Simplify/Condense	natural log of square root of x-1/5* natural log of x+ natural log of fourth root of x	$\ln (\sqrt{x}) - \frac{1}{5} \cdot \ln (x) + \ln (\sqrt[4]{x})$
22246	Simplify/Condense	natural log of square root of x+( natural log of x)/( natural log of y)+ natural log of y/x+1/2* natural log of x+ natural log of 1/y	$\ln (\sqrt{x}) + \frac{\ln (x)}{\ln (y)} + \ln (\frac{y}{x}) + \frac{1}{2} \cdot \ln (x) + \ln (\frac{1}{y})$
22247	Simplify/Condense	natural log of 16 root of x^9(x^8+9)	$\ln (\sqrt[16]{x^{9} (x^{8} + 9)})$
22248	Simplify/Condense	natural log of fourth root of (6x^3)/y	$\ln (\sqrt[4]{\frac{6 x^{3}}{y}})$
22249	Simplify/Condense	natural log of fourth root of 2	$\ln (\sqrt[4]{2})$
22250	Simplify/Condense	natural log of fourth root of 3- natural log of 9	$\ln (\sqrt[4]{3}) - \ln (9)$
22251	Simplify/Condense	natural log of fifth root of x^2y	$\ln (\sqrt[5]{x^{2} y})$
22252	Simplify/Condense	natural log of fifth root of 55	$\ln (\sqrt[5]{55})$
22253	Simplify/Condense	natural log of sixth root of e	$\ln (\sqrt[6]{e})$
22254	Simplify/Condense	natural log of seventh root of ey	$\ln (\sqrt[7]{e y})$
22255	Simplify/Condense	natural log of x/(e^(2x))	$\ln (\frac{x}{e^{2 x}})$
22256	Simplify/Condense	natural log of x/(e^(8x))	$\ln (\frac{x}{e^{8 x}})$
22257	Simplify/Condense	natural log of 6/(5x^6y)	$\ln (\frac{6}{5 x^{6} y})$
22258	Simplify/Condense	natural log of (6x)/y	$\ln (\frac{6 x}{y})$
22259	Simplify/Condense	natural log of 74/23	$\ln (\frac{74}{23})$
22260	Simplify/Condense	natural log of cos(x)^2+ natural log of 1+tan(x^2)	$\ln (\cos^{2} (x)) + \ln (1 + \tan (x^{2}))$
22261	Simplify/Condense	natural log of e^(-x^2*(3x))	$\ln (e^{- x^{2} \cdot (3 x)})$
22262	Simplify/Condense	natural log of e^11	$\ln (e^{11})$
22263	Simplify/Condense	natural log of e^2.50- natural log of square root of e	$\ln (e^{2.5}) - \ln (\sqrt{e})$
22264	Simplify/Condense	natural log of e^2+ natural log of e^5	$\ln (e^{2}) + \ln (e^{5})$
22265	Graph	y=-2cos(3x)	$y = - 2 \cos (3 x)$
22266	Simplify/Condense	natural log of 10.6/(29.8/28)	$\ln (\frac{10.6}{\frac{29.8}{28}})$
22267	Simplify/Condense	natural log of 10^3	$\ln (10^{3})$
22268	Simplify/Condense	natural log of (100e^10)/(7ex)	$\ln (\frac{100 e^{10}}{7 e x})$
22269	Simplify/Condense	natural log of (3x square root of 5-3x)/(3(x-4)^7)	$\ln (\frac{3 x \sqrt{5 - 3 x}}{3 {(x - 4)}^{7}})$
22270	Simplify/Condense	natural log of 4^x- natural log of 4^x	$\ln (4^{x}) - \ln (4^{x})$
22271	Simplify/Condense	natural log of (5x^2 cube root of 1-x)/(4(x+1)^2)	$\ln (\frac{5 x^{2} \sqrt[3]{1 - x}}{4 {(x + 1)}^{2}})$
22272	Simplify/Condense	natural log of 5/(e^7)	$\ln (\frac{5}{e^{7}})$
22273	Simplify/Condense	natural log of 5/6*0.182	$\ln (\frac{5}{6}) \cdot 0.182$
22274	Simplify/Condense	natural log of (5x-3)/(x+3)	$\ln (\frac{5 x - 3}{x + 3})$
22275	Simplify/Condense	6 natural log of z- natural log of w+4	$6 \ln (z) - \ln (w + 4)$
22276	Simplify/Condense	6 log of 811+12 log of 82	$6 \log (8) \cdot 11 + 12 \log (8) \cdot 2$
22277	Simplify/Condense	6 log of 8-30 log of 11	$6 \log (8) - 30 \log (11)$
22278	Simplify/Condense	6 log of u+ log of v	$6 \log (u) + \log (v)$
22279	Simplify/Condense	6 log of w-1/3* log of z+5 log of y	$6 \log (w) - \frac{1}{3} \cdot \log (z) + 5 \log (y)$
22280	Simplify/Condense	6 log of x+4 log of y	$6 \log (x) + 4 \log (y)$
22281	Simplify/Condense	6 log of x+5 log of x-8	$6 \log (x) + 5 \log (x - 8)$
22282	Simplify/Condense	6 log of x+ log of y- log of z	$6 \log (x) + \log (y) - \log (z)$
22283	Simplify/Condense	6 log of x9+9 log of x5^9	$6 \log (x) \cdot 9 + 9 \log (x) \cdot 5^{9}$
22284	Simplify/Condense	7 log base 5 of u+5 log base 5 of v	$7 \log_{5} (u) + 5 \log_{5} (v)$
22285	Simplify/Condense	7 log base 5 of x+2 log base 5 of x	$7 \log_{5} (x) + 2 \log_{5} (x)$
22286	Simplify/Condense	7 log base 5 of y+1/4*( log base 5 of z-3 log base 5 of 5w)	$7 \log_{5} (y + \frac{1}{4} \cdot (\log_{5} (z - 3) \log_{5} (5 w)))$
22287	Simplify/Condense	7 log base 5 of z-3-4 log base 5 of z+8	$7 \log_{5} (z - 3) - 4 \log_{5} (z + 8)$
22288	Simplify/Condense	7 log base 5 of z-7-6 log base 5 of z+4	$7 \log_{5} (z - 7) - 6 \log_{5} (z + 4)$
22289	Simplify/Condense	7 log base 7 of 5x-4	$7 \log_{7} (5 x - 4)$
22290	Simplify/Condense	7 log base 7 of 6w+1+1/2* log base 7 of w+6	$7 \log_{7} (6 w + 1) + \frac{1}{2} \cdot \log_{7} (w + 6)$
22291	Simplify/Condense	7 log base 8 of y-1/5* log base 8 of y+3 log base 8 of w	$7 \log_{8} (y) - \frac{1}{5} \cdot \log_{8} (y) + 3 \log_{8} (w)$
22292	Simplify/Condense	7 log base a of 5+4 log base a of 3	$7 \log_{a} (5) + 4 \log_{a} (3)$
22293	Simplify/Condense	7 log base b of 8+9 log base b of 10	$7 \log_{b} (8) + 9 \log_{b} (10)$
22294	Graph	r=2+3sin(theta)	$r = 2 + 3 \sin (θ)$
22295	Simplify/Condense	7 log base x of y-3 log base x of z^2	$7 \log_{x} (y) - 3 \log_{x} (z^{2})$
22296	Simplify/Condense	78-15 log of t+1	$78 - 15 \log (t + 1)$
22297	Simplify/Condense	7 natural log of x-1/9* natural log of y	$7 \ln (x) - \frac{1}{9} \cdot \ln (y)$
22298	Simplify/Condense	natural log of (e^5)/(x^2)	$\ln (\frac{e^{5}}{x^{2}})$
22299	Simplify/Condense	natural log of (e^5)/8	$\ln (\frac{e^{5}}{8})$
22300	Simplify/Condense	natural log of (x^(1/3) square root of x^4-x)/(e^(2x))	$\ln (\frac{x^{\frac{1}{3}} \sqrt{x^{4} - x}}{e^{2 x}})$