Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
22101	Simplify/Condense	(e)( natural log of 2x+1)	$(e) (\ln (2 x + 1))$
22102	Simplify/Condense	(k+1)k(k-1)	$(k + 1) k (k - 1)$
22103	Simplify/Condense	natural log of sin(g)+ natural log of le- natural log of d-u natural log of x-le natural log of b	$\ln (\sin (g)) + \ln (l e) - \ln (d) - u \ln (x) - l e \ln (b)$
22104	Simplify/Condense	( natural log of x-(x+5))(5)	$(\ln (x) - (x + 5)) (5)$
22105	Simplify/Condense	( natural log of x)(6x^5)	$(\ln (x)) (6 x^{5})$
22106	Simplify/Condense	-( log of 3.9+ log of 10^-4)	$- (\log (3.9) + \log (10^{- 4}))$
22107	Simplify/Condense	log base 3 of (3)^(5x)	$\log_{3} ({(3)}^{5 x})$
22108	Simplify/Condense	log base 3 of (5)^3+ log base 3 of 25	$\log_{3} ({(5)}^{3}) + \log_{3} (25)$
22109	Simplify/Condense	log base 32 of (4)^1.5+10^(2 log of 2)	$\log_{32} ({(4)}^{1.5}) + 10^{2 \log (2)}$
22110	Simplify/Condense	log base 4 of (16/(x^2y))^3	$\log_{4} ({(\frac{16}{x^{2} y})}^{3})$
22111	Simplify/Condense	log base 4 of (3)^4+ log base 4 of 9	$\log_{4} ({(3)}^{4}) + \log_{4} (9)$
22112	Simplify/Condense	log base 4 of (4)^(-3y^2)	$\log_{4} ({(4)}^{- 3 y^{2}})$
22113	Simplify/Condense	( log base 4 of 49)/( log base 4 of 7)	$\frac{\log_{4} (49)}{\log_{4} (7)}$
22114	Simplify/Condense	log base 4 of (5)^4+ log base 4 of 25	$\log_{4} ({(5)}^{4}) + \log_{4} (25)$
22115	Simplify/Condense	( log base 4 of 64)/( log base 9 of 1)	$\frac{\log_{4} (64)}{\log_{9} (1)}$
22116	Simplify/Condense	log base 4 of (xy)^3- log base 4 of xy	$\log_{4} ({(x y)}^{3}) - \log_{4} (x y)$
22117	Simplify/Condense	log base 2 of (8)^3.1	$\log_{2} ({(8)}^{3.1})$
22118	Simplify/Condense	log base 3 of (1/27)^4	$\log_{3} ({(\frac{1}{27})}^{4})$
22119	Simplify/Condense	log base 3 of (2/m)^3	$\log_{3} ({(\frac{2}{m})}^{3})$
22120	Simplify/Condense	( log of x)*( log of 2)	$(\log (x)) \cdot (\log (2))$
22121	Simplify/Condense	log of 100+ log base x of square root of x- natural log of e^3	$\log (100) + \log_{x} (\sqrt{x}) - \ln (e^{3})$
22122	Simplify/Condense	( natural log of 30- natural log of 3)/( natural log of 100- natural log of 1)+ natural log of 9-1/2* natural log of 10* log of 9	$\frac{\ln (30) - \ln (3)}{\ln (100 - \ln (1))} + \ln (9) - \frac{1}{2} \cdot \ln (10) \cdot \log (9)$
22123	Simplify/Condense	( log of x-6(x))/( log of 4)-2	$\frac{\log (x - 6) (x)}{\log (4)} - 2$
22124	Simplify/Condense	log base 4 of x^2-49-4 log base 4 of x+7	$\log_{4} (x^{2} - 49) - 4 \log_{4} (x + 7)$
22125	Simplify/Condense	log base 7 of (2)^4+ log of (7)^4	$\log_{7} ({(2)}^{4}) + \log ({(7)}^{4})$
22126	Simplify/Condense	1/4*(( natural log of 93)/4-( natural log of 24)/4)	$\frac{1}{4} \cdot (\frac{\ln (93)}{4} - \frac{\ln (24)}{4})$
22127	Simplify/Condense	((3x^(3/2))/2-6x^(3/2))/(9x^4)-(6x^(1/2)-9x^(1/2) natural log of x)/(36x^3)	$\frac{\frac{3 x^{\frac{3}{2}}}{2} - 6 x^{\frac{3}{2}}}{9 x^{4}} - \frac{6 x^{\frac{1}{2}} - 9 x^{\frac{1}{2}} \ln (x)}{36 x^{3}}$
22128	Simplify/Condense	(8^( log of x-2))/8	$\frac{8^{\log (x - 2)}}{8}$
22129	Simplify/Condense	log base 2 of (2)^0.3	$\log_{2} ({(2)}^{0.3})$
22130	Simplify/Condense	log base 2 of (2)^69	$\log_{2} ({(2)}^{69})$
22131	Simplify/Condense	log base 2 of (2xy)^(1/2)	$\log_{2} ({(2 x y)}^{\frac{1}{2}})$
22132	Simplify/Condense	log base 2 of (4x-5)^2	$\log_{2} ({(4 x - 5)}^{2})$
22133	Simplify/Condense	log of x- log of x+3+ log of x^2-9	$\log (x) - \log (x + 3) + \log (x^{2} - 9)$
22134	Simplify/Condense	log of x+1/7 log of y^2-6 log of z	$\log (x + \frac{1}{7}) \log (y^{2}) - 6 \log (z)$
22135	Simplify/Condense	log of x+1-2 log of x-2-3 log of y	$\log (x + 1) - 2 \log (x - 2) - 3 \log (y)$
22136	Simplify/Condense	log of x+25=1+ log of 2x-7	$\log (x + 25) = 1 + \log (2 x - 7)$
22137	Simplify/Condense	log of x+3-4 log of x	$\log (x + 3) - 4 \log (x)$
22138	Find the Exact Value	cot(6pi)	$\cot (6 π)$
22139	Simplify/Condense	( square root of 10)^( log of 9)	${(\sqrt{10})}^{\log (9)}$
22140	Simplify/Condense	( square root of natural log of 9-x)/( square root of natural log of 9-x- square root of natural log of x+3)	$\frac{\sqrt{\ln (9 - x)}}{\sqrt{\ln (9 - x)} - \sqrt{\ln (x + 3)}}$
22141	Simplify/Condense	(x^(-1/2)*(2^(x^(1/2)) natural log of 2))/2	$\frac{x^{- \frac{1}{2}} \cdot (2^{x^{\frac{1}{2}}} \ln (2))}{2}$
22142	Simplify/Condense	0.01/(1.00+0.50)( log of 8141.333)/100	$\frac{0.01}{1 + 0.5} \cdot \frac{\log (8) \cdot 141.333}{100}$
22143	Simplify/Condense	-1/0.03* natural log of 1/4	$- \frac{1}{0.03} \cdot \ln (\frac{1}{4})$
22144	Simplify/Condense	1/(4^7)-(6 natural log of 4)/(4^7)	$\frac{1}{4^{7}} - \frac{6 \ln (4)}{4^{7}}$
22145	Simplify/Condense	1/( log base 2 of 6)+1/( log base 3 of 6)	$\frac{1}{\log_{2} (6)} + \frac{1}{\log_{3} (6)}$
22146	Simplify/Condense	1/( log base 4 of p)+1/( log base 3 of p)	$\frac{1}{\log_{4} (p)} + \frac{1}{\log_{3} (p)}$
22147	Simplify/Condense	1/0.000013* natural log of 1.225/((3)*(1100(0.000013)sin(12)))	$\frac{1}{0.000013} \cdot \ln (\frac{1.225}{(3) \cdot (1100 (0.000013) \sin (12))})$
22148	Simplify/Condense	1/0.002* natural log of 1220	$\frac{1}{0.002} \cdot \ln (1220)$
22149	Simplify/Condense	-1/0.002* natural log of 1220	$- \frac{1}{0.002} \cdot \ln (1220)$
22150	Simplify/Condense	1/(1+ log base c of ab)+1/(1+ log base a of bc)+1/(1+ log base b of ca)	$\frac{1}{1 + \log_{c} (a b)} + \frac{1}{1 + \log_{a} (b c)} + \frac{1}{1 + \log_{b} (c a)}$
22151	Simplify/Condense	-1/10* natural log of 54/79	$- \frac{1}{10} \cdot \ln (\frac{54}{79})$
22152	Simplify/Condense	1/10* log of x	$\frac{1}{10} \cdot \log (x)$
22153	Simplify/Condense	1/14* log of 8.42+10 log of 2463	$\frac{1}{14} \cdot \log (8.42) + 10 \log (2463)$
22154	Simplify/Condense	1/1690*( natural log of 1/2)	$\frac{1}{1690} \cdot (\ln (\frac{1}{2}))$
22155	Simplify/Condense	1/1690* natural log of 10	$\frac{1}{1690} \cdot \ln (10)$
22156	Simplify/Condense	1/2*(( log base 7 of ab)/(5 log base 7 of c))	$\frac{1}{2} \cdot (\frac{\log_{7} (a b)}{5 \log_{7} (c)})$
22157	Simplify/Condense	1/2*(( natural log of 7)/( natural log of x))	$\frac{1}{2} \cdot (\frac{\ln (7)}{\ln (x)})$
22158	Simplify/Condense	1/2*( log of (7)^s+ log of (7)^t)	$\frac{1}{2} \cdot (\log ({(7)}^{s}) + \log ({(7)}^{t}))$
22159	Simplify/Condense	1/2*( log base 2 of a+ log base 2 of b)	$\frac{1}{2} \cdot (\log_{2} (a) + \log_{2} (b))$
22160	Simplify/Condense	1/2*( log base 2 of s+ log base 2 of t)	$\frac{1}{2} \cdot (\log_{2} (s) + \log_{2} (t))$
22161	Simplify/Condense	1/2*( log base 2 of x+ log base 2 of y)-3 log base 2 of x+7	$\frac{1}{2} \cdot (\log_{2} (x) + \log_{2} (y)) - 3 \log_{2} (x + 7)$
22162	Simplify/Condense	1/2*( log base 4 of a)+ log base 4 of b	$\frac{1}{2} \cdot (\log_{4} (a)) + \log_{4} (b)$
22163	Simplify/Condense	1/2*( log base 4 of x- log base 4 of y-5 log base 4 of x+8)	$\frac{1}{2} \cdot (\log_{4} (x) - \log_{4} (y) - 5 \log_{4} (x + 8))$
22164	Simplify/Condense	log base 9 of (x)^2(x-2)	$\log_{9} ({(x)}^{2} (x - 2))$
22165	Simplify/Condense	log base 7 of (7)^x	$\log_{7} ({(7)}^{x})$
22166	Simplify/Condense	log base 7 of (7m^2)^(-2/3)+ log base 7 of (49m^2)^(1/2)	$\log_{7} ({(7 m^{2})}^{- \frac{2}{3}}) + \log_{7} ({(49 m^{2})}^{\frac{1}{2}})$
22167	Simplify/Condense	( log base 7 of x)/2+( log base 7 of y)/2+( log base 7 of z)/2	$\frac{\log_{7} (x)}{2} + \frac{\log_{7} (y)}{2} + \frac{\log_{7} (z)}{2}$
22168	Simplify/Condense	( log base 5 of 1)/250	$\frac{\log_{5} (1)}{250}$
22169	Simplify/Condense	( log base 5 of 16)/( log base 5 of 4)	$\frac{\log_{5} (16)}{\log_{5} (4)}$
22170	Simplify/Condense	log base 5 of (z)^8	$\log_{5} ({(z)}^{8})$
22171	Simplify/Condense	log base 6 of (z/36)^4	$\log_{6} ({(\frac{z}{36})}^{4})$
22172	Simplify/Condense	natural log of 10- natural log of 5-1/3* natural log of 8	$\ln (10) - \ln (5) - \frac{1}{3} \cdot \ln (8)$
22173	Simplify/Condense	natural log of 0.0236	$\ln (0.0236)$
22174	Simplify/Condense	natural log of 0.2b	$\ln (0.2 b)$
22175	Simplify/Condense	natural log of 1x^2+ natural log of 1(x-1) natural log of 1(x+1)	$\ln (1) x^{2} + \ln (1) (x - 1) \ln (1) (x + 1)$
22176	Simplify/Condense	natural log of 1+sin(x)- natural log of \|sec(x)\|	$\ln (1 + \sin (x)) - \ln (\| \sec (x) \|)$
22177	Simplify/Condense	natural log of 1+sin(x)- natural log of \|sin(x)\|	$\ln (1 + \sin (x)) - \ln (\| \sin (x) \|)$
22178	Simplify/Condense	natural log of x^8y^2z	$\ln (x^{8} y^{2} z)$
22179	Simplify/Condense	natural log of (x-1)/x+ natural log of x/(x+1)- natural log of x^2-1	$\ln (\frac{x - 1}{x}) + \ln (\frac{x}{x + 1}) - \ln (x^{2} - 1)$
22180	Simplify/Condense	natural log of (x-2)/(e^(7x))	$\ln (\frac{x - 2}{e^{7 x}})$
22181	Simplify/Condense	natural log of (xy)/z	$\ln (\frac{x y}{z})$
22182	Simplify/Condense	natural log of xyz^4	$\ln (x y z^{4})$
22183	Simplify/Condense	natural log of x^6-4 natural log of 4 square root of x^5	$\ln (x^{6} - 4) \ln (4 \sqrt{x^{5}})$
22184	Simplify/Condense	natural log of x^4-5 natural log of fifth root of x^3	$\ln (x^{4}) - 5 \ln (\sqrt[5]{x^{3}})$
22185	Simplify/Condense	natural log of x^(4x)+6x^(2x)-16	$\ln (x^{4 x} + 6 x^{2 x} - 16)$
22186	Simplify/Condense	natural log of x/(x-1)- natural log of x^2-1	$\ln (\frac{x}{x - 1}) - \ln (x^{2} - 1)$
22187	Simplify/Condense	natural log of x^3+ natural log of fourth root of y^3- natural log of 1000+ natural log of square root of w	$\ln (x^{3}) + \ln (\sqrt[4]{y^{3}}) - \ln (1000) + \ln (\sqrt{w})$
22188	Simplify/Condense	natural log of square root of (x^2)/(y^5)	$\ln (\sqrt{\frac{x^{2}}{y^{5}}})$
22189	Simplify/Condense	natural log of square root of (x^6)/(y^7)	$\ln (\sqrt{\frac{x^{6}}{y^{7}}})$
22190	Find the Vertex	f(x)=9-(x-4)^2	$f (x) = 9 - {(x - 4)}^{2}$
22191	Simplify/Condense	natural log of e^7x+9+4 natural log of e^3x+1	$\ln (e^{7} x + 9) + 4 \ln (e^{3} x + 1)$
22192	Simplify/Condense	natural log of e^(2x) square root of x	$\ln (e^{2 x} \sqrt{x})$
22193	Simplify/Condense	natural log of e^3- natural log of e^7	$\ln (e^{3}) - \ln (e^{7})$
22194	Simplify/Condense	natural log of e^3x^2- natural log of ey^5+1	$\ln (e^{3} x^{2}) - \ln (e y^{5}) + 1$
22195	Simplify/Condense	natural log of e^3y+ natural log of ey-4	$\ln (e^{3} y) + \ln (e y) - 4$
22196	Simplify/Condense	natural log of x/(x-6)+ natural log of (x+6)/x- natural log of x^2-36	$\ln (\frac{x}{x - 6}) + \ln (\frac{x + 6}{x}) - \ln (x^{2} - 36)$
22197	Simplify/Condense	natural log of x/(x-8)+ natural log of (x+8)/x- natural log of x^2-64	$\ln (\frac{x}{x - 8}) + \ln (\frac{x + 8}{x}) - \ln (x^{2} - 64)$
22198	Simplify/Condense	natural log of x/(x-9)+ natural log of (x+9)/x- natural log of x^2-81	$\ln (\frac{x}{x - 9}) + \ln (\frac{x + 9}{x}) - \ln (x^{2} - 81)$
22199	Simplify/Condense	natural log of x^10+ natural log of square root of 3-x	$\ln (x^{10}) + \ln (\sqrt{3 - x})$
22200	Simplify/Condense	natural log of x^2+5 natural log of 2x	$\ln (x^{2}) + 5 \ln (2 x)$