Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
21801	Simplify/Condense	natural log of 2- natural log of 1	$\ln (2) - \ln (1)$
21802	Simplify/Condense	natural log of 13- natural log of 1	$\ln (13) - \ln (1)$
21803	Simplify/Condense	natural log of 2- natural log of 5	$\ln (2) - \ln (5)$
21804	Simplify/Condense	natural log of 10- natural log of 1	$\ln (10) - \ln (1)$
21805	Simplify/Condense	natural log of 2x- natural log of x	$\ln (2 x) - \ln (x)$
21806	Simplify/Condense	log of 212- log of 23^2	$\log (2) \cdot 12 - \log (2) \cdot 3^{2}$
21807	Simplify/Condense	natural log of x(x+2)(x+1)	$\ln (x) (x + 2) (x + 1)$
21808	Expand the Logarithmic Expression	( natural log of 128)/((7pi)/2)	$\frac{\ln (128)}{\frac{7 π}{2}}$
21809	Expand the Logarithmic Expression	natural log of ((x^2-2)/(x^3))^2	$\ln ({(\frac{x^{2} - 2}{x^{3}})}^{2})$
21810	Expand the Logarithmic Expression	( natural log of 4/9)/-0.5	$\frac{\ln (\frac{4}{9})}{- 0.5}$
21811	Expand the Logarithmic Expression	( natural log of 2)/8	$\frac{\ln (2)}{8}$
21812	Expand the Logarithmic Expression	12/( natural log of 12)-(12^-1)/( natural log of 12)	$\frac{12}{\ln (12)} - \frac{12^{- 1}}{\ln (12)}$
21813	Expand the Logarithmic Expression	log base 2 of 4y^4	$\log_{2} (4 y^{4})$
21814	Expand the Logarithmic Expression	log base 2 of 1024	$\log_{2} (1024)$
21815	Expand the Logarithmic Expression	log base 2 of x^4y^3	$\log_{2} (x^{4} y^{3})$
21816	Expand the Logarithmic Expression	log base 3 of 36x+27y	$\log_{3} (36 x + 27 y)$
21817	Expand the Logarithmic Expression	log base 8 of 320- log base 8 of 5	$\log_{8} (320) - \log_{8} (5)$
21818	Expand the Logarithmic Expression	log base 4 of 320- log base 4 of 5	$\log_{4} (320) - \log_{4} (5)$
21819	Expand the Logarithmic Expression	log base 5 of cube root of 25	$\log_{5} (\sqrt[3]{25})$
21820	Expand the Logarithmic Expression	natural log of 2x^3(x-3)	$\ln (2 x^{3} (x - 3))$
21821	Expand the Logarithmic Expression	log of M^-8	$\log (M^{- 8})$
21822	Expand the Logarithmic Expression	sin(h( natural log of 3))	$\sinh (\ln (3))$
21823	Expand the Logarithmic Expression	log of 2x^4	$\log (2 x^{4})$
21824	Expand the Logarithmic Expression	log of (x(x+2))/((x+6)^5)	$\log (\frac{x (x + 2)}{{(x + 6)}^{5}})$
21825	Expand the Logarithmic Expression	log of 512	$\log (512)$
21826	Expand the Logarithmic Expression	natural log of square root of 10t^25v^2	$\ln (\sqrt{10 t^{25} v^{2}})$
21827	Expand the Logarithmic Expression	natural log of x/( square root of x^4y^4)	$\ln (\frac{x}{\sqrt{x^{4} y^{4}}})$
21828	Expand the Logarithmic Expression	natural log of x/( square root of x^6y^2)	$\ln (\frac{x}{\sqrt{x^{6} y^{2}}})$
21829	Expand the Logarithmic Expression	natural log of square root of a-1	$\ln (\sqrt{a - 1})$
21830	Expand the Logarithmic Expression	natural log of (9x)/( square root of x^2-4)	$\ln (\frac{9 x}{\sqrt{x^{2} - 4}})$
21831	Expand the Logarithmic Expression	natural log of cube root of 3r^2s	$\ln (\sqrt[3]{3 r^{2} s})$
21832	Expand the Logarithmic Expression	natural log of 3/2	$\ln (\frac{3}{2})$
21833	Expand the Logarithmic Expression	natural log of (5x)/(y^2)	$\ln (\frac{5 x}{y^{2}})$
21834	Expand the Logarithmic Expression	natural log of (7 square root of 5)/( cube root of 3)	$\ln (\frac{7 \sqrt{5}}{\sqrt[3]{3}})$
21835	Expand the Logarithmic Expression	natural log of 3125/4-3	$\ln (\frac{3125}{4}) - 3$
21836	Expand the Logarithmic Expression	natural log of e^y-2xe^y	$\ln (e^{y} - 2 x e^{y})$
21837	Expand the Logarithmic Expression	natural log of (2 square root of 5)/( cube root of 7)	$\ln (\frac{2 \sqrt{5}}{\sqrt[3]{7}})$
21838	Expand the Logarithmic Expression	96-14 log of 0+2	$96 - 14 \log (0 + 2)$
21839	Expand the Logarithmic Expression	natural log of (x^2(3x-5))/(3(2x+1)e^(7x))	$\ln (\frac{x^{2} (3 x - 5)}{3 (2 x + 1) e^{7 x}})$
21840	Expand the Logarithmic Expression	log base a of fourth root of (m^8n^12)/(a^3b^5)	$\log_{a} (\sqrt[4]{\frac{m^{8} n^{12}}{a^{3} b^{5}}})$
21841	Expand the Logarithmic Expression	log base b of 2x^2y^3	$\log_{b} (2 x^{2} y^{3})$
21842	Expand the Logarithmic Expression	log base 9 of (xy^3)/(z^2)	$\log_{9} (\frac{x y^{3}}{z^{2}})$
21843	Expand the Logarithmic Expression	2 natural log of 2	$2 \ln (2)$
21844	Write in Exponential Form	log base 49 of 1/7=y	$\log_{49} (\frac{1}{7}) = y$
21845	Write in Exponential Form	log base x of 125=3/4	$\log_{x} (125) = \frac{3}{4}$
21846	Write in Exponential Form	z^n=e^(n natural log of z)	$z^{n} = e^{n \ln (z)}$
21847	Write in Exponential Form	0=2^x+2^xx natural log of 2	$0 = 2^{x} + 2^{x} x \ln (2)$
21848	Solve for x	log of 381=x	$\log (381) = x$
21849	Expand the Logarithmic Expression	log of x(x^5+8)^(-1/2)	$\log (x {(x^{5} + 8)}^{- \frac{1}{2}})$
21850	Solve for x	natural log of e^x-2=3	$\ln (e^{x} - 2) = 3$
21851	Write in Exponential Form	( log of 3x+5)/( log of 4)=3	$\frac{\log (3 x + 5)}{\log (4)} = 3$
21852	Write in Exponential Form	( natural log of 2)/0.13=t	$\frac{\ln (2)}{0.13} = t$
21853	Solve for x	2x = natural log of 3x^2	$2 x = \ln (3 x^{2})$
21854	Write in Exponential Form	e^( natural log of x)=4	$e^{\ln (x)} = 4$
21855	Write in Exponential Form	f^4(x) = natural log of x	$f^{4} (x) = \ln (x)$
21856	Write in Exponential Form	( natural log of 2)/0.02=t	$\frac{\ln (2)}{0.02} = t$
21857	Write in Exponential Form	log base 2 of kx=a	$\log_{2} (k x) = a$
21858	Write in Exponential Form	y = log of 1000	$y = \log (1000)$
21859	Write in Exponential Form	natural log of y=( natural log of x^2-3)/2	$\ln (y) = \frac{\ln (x^{2} - 3)}{2}$
21860	Write in Exponential Form	log of 2(x^2+3x-50)=2	$\log (2) (x^{2} + 3 x - 50) = 2$
21861	Find dy/dx	x^3+y^3=2	$x^{3} + y^{3} = 2$
21862	Write in Exponential Form	natural log of 4x-3+ natural log of x-5 = natural log of 15	$\ln (4 x - 3) + \ln (x - 5) = \ln (15)$
21863	Write in Exponential Form	natural log of 5-2x=3	$\ln (5 - 2 x) = 3$
21864	Write in Exponential Form	2 natural log of 8x=10	$2 \ln (8 x) = 10$
21865	Write in Exponential Form	2 natural log of x-1/3* natural log of x^2=4	$2 \ln (x) - \frac{1}{3} \cdot \ln (x^{2}) = 4$
21866	Write in Exponential Form	natural log of 3x-11=7	$\ln (3 x - 11) = 7$
21867	Write in Exponential Form	log base 27 of x-1 = log base 81 of 2x+3	$\log_{27} (x - 1) = \log_{81} (2 x + 3)$
21868	Write in Exponential Form	natural log of 0.381=3000x+ natural log of 5	$\ln (0.381) = 3000 x + \ln (5)$
21869	Write in Exponential Form	natural log of 7+2x = natural log of 1+4x	$\ln (7 + 2 x) = \ln (1 + 4 x)$
21870	Write in Exponential Form	natural log of x-x=0	$\ln (x) - x = 0$
21871	Find dy/dx	x^(6/7)+y^(8/5)=9	$x^{\frac{6}{7}} + y^{\frac{8}{5}} = 9$
21872	Find dy/dx	y^2=1/(1-x^2)	$y^{2} = \frac{1}{1 - x^{2}}$
21873	Find the Midpoint	(0,800) , (3,3200)	$(0, 800)$ , $(3, 3200)$
21874	Evaluate the Limit	limit as x approaches 2 of sin((pix)/2)	$lim_{x \to 2} \sin (\frac{π x}{2})$
21875	Find the Midpoint	(-2,5) , (0,-7)	$(- 2, 5)$ , $(0, - 7)$
21876	Find the Distance Between Two Points	(-2/3,3/2) , (7/3,2)	$(- \frac{2}{3}, \frac{3}{2})$ , $(\frac{7}{3}, 2)$
21877	Find the Distance Between Two Points	(2,-2) , (7,9)	$(2, - 2)$ , $(7, 9)$
21878	Find the Distance Between Two Points	(4,-3) , (2,-8)	$(4, - 3) (2, - 8)$
21879	Find the Distance Between Two Points	(3,-54) , (-3,54)	$(3, - 54)$ , $(- 3, 54)$
21880	Find the Distance Between Two Points	(-4,-3) , (-6,-2)	$(- 4, - 3) (- 6, - 2)$
21881	Find the Midpoint	(-3,-2) , (1,6)	$(- 3, - 2)$ , $(1, 6)$
21882	Find the Distance Between Two Points	(17,5) , (5,0)	$(17, 5)$ , $(5, 0)$
21883	Find the Distance Between Two Points	a=(-4,2) , b=(1,5)	$a = (- 4, 2)$ , $b = (1, 5)$
21884	Eliminate the Parameter	x=4t+2 , y=t^2	$x = 4 t + 2$ , $y = t^{2}$
21885	Eliminate the Parameter	x=t^2+3 , y=t^2-2	$x = t^{2} + 3$ , $y = t^{2} - 2$
21886	Eliminate the Parameter	x=1+t , y=4-4t	$x = 1 + t$ , $y = 4 - 4 t$
21887	Evaluate the Limit	limit as t approaches infinity of ( square root of t+t^2)/(6t-t^2)	$lim_{t \to \infty} \frac{\sqrt{t} + t^{2}}{6 t - t^{2}}$
21888	Find the Intersection of the Inequalities	x+3y>-5 , 4x+y=5	$x + 3 y > - 5$ , $4 x + y = 5$
21889	Convert to Polar Coordinates	(2,3)	$(2, 3)$
21890	Convert to Rectangular Coordinates	(-5,-pi/6)	$(- 5, - \frac{π}{6})$
21891	Convert to Polar Coordinates	(3,-5)	$(3, - 5)$
21892	Convert to Rectangular Coordinates	(-1,- square root of 3)	$(- 1, - \sqrt{3})$
21893	Determine if @POINT is a Solution	y=4x^3-4x , (1,0)	$y = 4 x^{3} - 4 x$ , $(1, 0)$
21894	Determine if @POINT is a Solution	y=3x^3-2x , (1,1)	$y = 3 x^{3} - 2 x$ , $(1, 1)$
21895	Determine if @POINT is a Solution	y=x^3-3x , (2,2)	$y = x^{3} - 3 x$ , $(2, 2)$
21896	Determine if @POINT is a Solution	y=2x^3-3x , (1,-1)	$y = 2 x^{3} - 3 x$ , $(1, - 1)$
21897	Determine if @POINT is a Solution	2(x)^2+y^2=41 , (4,3)	$2 {(x)}^{2} + y^{2} = 41$ , $(4, 3)$
21898	Simplify/Condense	natural log of 5+1/2* natural log of x+3-3 natural log of 1+ square root of x	$\ln (5) + \frac{1}{2} \cdot \ln (x + 3) - 3 \ln (1 + \sqrt{x})$
21899	Simplify/Condense	natural log of 1+x^2+1/2* natural log of x- natural log of sin(x)	$\ln (1 + x^{2}) + \frac{1}{2} \cdot \ln (x) - \ln (\sin (x))$
21900	Simplify/Condense	1/2* natural log of x+8 natural log of y-3 natural log of z	$\frac{1}{2} \cdot \ln (x) + 8 \ln (y) - 3 \ln (z)$