Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
54601	Write as a Single Logarithm	1/2 log of x-3 log of sin(2x)+2	$\frac{1}{2} \log (x) - 3 \log (\sin (2 x)) + 2$
54602	Write as a Single Logarithm	log base 3 of 6^3*9^6	$\log_{3} (6^{3} \cdot 9^{6})$
54603	Write as a Single Logarithm	log of 7-2 log of 12	$\log (7) - 2 \log (12)$
54604	Write as a Single Logarithm	natural log of x-3+ natural log of x+1 = natural log of x+7	$\ln (x - 3) + \ln (x + 1) = \ln (x + 7)$
54605	Write as a Single Logarithm	log base 9 of 3+3 log base 9 of 2	$\log_{9} (3) + 3 \log_{9} (2)$
54606	Find the Concavity	f(x)=x^3-8x^2-12x+6	$f (x) = x^{3} - 8 x^{2} - 12 x + 6$
54607	Find the Concavity	f(x)=x^3-4x^2+5x	$f (x) = x^{3} - 4 x^{2} + 5 x$
54608	Find the Concavity	f(x)=(x+1)/(x^2-4x-5)	$f (x) = \frac{x + 1}{x^{2} - 4 x - 5}$
54609	Find the Concavity	f(x)=(x^2)/(x^2-81)	$f (x) = \frac{x^{2}}{x^{2} - 81}$
54610	Find the Concavity	f(x)=x^3-9x^2+26x-24	$f (x) = x^{3} - 9 x^{2} + 26 x - 24$
54611	Find the Concavity	f(x)=x^3-4x^2-16x+7	$f (x) = x^{3} - 4 x^{2} - 16 x + 7$
54612	Find the Concavity	f(x)=(5 natural log of x)/x	$f (x) = \frac{(5 \ln (x))}{x}$
54613	Find the Concavity	f(x)=x^4-20x^3+150x^2-1	$f (x) = x^{4} - 20 x^{3} + 150 x^{2} - 1$
54614	Find the Concavity	f(x)=e^(8x)+e^(-x)	$f (x) = e^{8 x} + e^{- x}$
54615	Find the Concavity	f(x)=x^3-4x^2-16x+2	$f (x) = x^{3} - 4 x^{2} - 16 x + 2$
54616	Find the Concavity	f(x)=x^3-6x^2+28x-40	$f (x) = x^{3} - 6 x^{2} + 28 x - 40$
54617	Find the Concavity	f(x)=36e^x-e^(2x)	$f (x) = 36 e^{x} - e^{2 x}$
54618	Find the Concavity	f(x)=x^3-3x^2+29x-27	$f (x) = x^{3} - 3 x^{2} + 29 x - 27$
54619	Find the Concavity	f(x)=(2x+2)/((x+4)^2)	$f (x) = \frac{2 x + 2}{{(x + 4)}^{2}}$
54620	Find the Concavity	f(x)=(x+1)^3(x+2)^2	$f (x) = {(x + 1)}^{3} {(x + 2)}^{2}$
54621	Find the Concavity	f(x)=(x+1)/(x^2-5x-6)	$f (x) = \frac{x + 1}{x^{2} - 5 x - 6}$
54622	Find the Concavity	f(x)=x^3-9x^2+21x-9	$f (x) = x^{3} - 9 x^{2} + 21 x - 9$
54623	Find the Concavity	f(x)=x square root of 18-x	$f (x) = x \sqrt{18 - x}$
54624	Find the Concavity	f(x)=x^3-6x^2+27x-38	$f (x) = x^{3} - 6 x^{2} + 27 x - 38$
54625	Find the Concavity	f(x)=-8/(x-8)	$f (x) = - \frac{8}{(x - 8)}$
54626	Find the Concavity	f(x)=15/(x^2+12)	$f (x) = \frac{15}{x^{2} + 12}$
54627	Find the Concavity	f(x)=3x^5-10x^4+2x-5	$f (x) = 3 x^{5} - 10 x^{4} + 2 x - 5$
54628	Find the Slope	y=4x+10	$y = 4 x + 10$
54629	Find the Slope	y=7x-3	$y = 7 x - 3$
54630	Find the Slope	y=3-x	$y = 3 - x$
54631	Find the Slope	y=(2x+3)/4	$y = \frac{2 x + 3}{4}$
54632	Find the Slope	(-1,5) , (3,4)	$(- 1, 5) (3, 4)$
54633	Find the Slope	y=0.5x	$y = 0.5 x$
54634	Find the Slope	y=7x+8	$y = 7 x + 8$
54635	Find the Slope	9x-3y=15	$9 x - 3 y = 15$
54636	Find the Slope	2x+4y=24	$2 x + 4 y = 24$
54637	Find the Slope	21x+3y=7	$21 x + 3 y = 7$
54638	Find f(g(x))	f(x)=2x^2-7 , g(x)=8/x	$f (x) = 2 x^{2} - 7$ , $g (x) = \frac{8}{x}$
54639	Find f(g(x))	f(x)=x^2-1 , g(x)=sin(x)	$f (x) = x^{2} - 1$ , $g (x) = \sin (x)$
54640	Find f(g(x))	f(x)=\|x\| , g(x)=x	$f (x) = \| x \|$ , $g (x) = x$
54641	Find g(f(x))	f(x)=x/10+3 , g(x)=8x-1	$f (x) = \frac{x}{10} + 3$ , $g (x) = 8 x - 1$
54642	Find g(f(x))	f(x)=(e^x)/4 ; g(x)=x^2	$f (x) = \frac{e^{x}}{4}$ ; $g (x) = x^{2}$
54643	Find g(f(x))	f(x)=x/10+7 , g(x)=8x-1	$f (x) = \frac{x}{10} + 7$ , $g (x) = 8 x - 1$
54644	Find g(f(x))	f(x)=x/6+7 , g(x)=4x-1	$f (x) = \frac{x}{6} + 7$ , $g (x) = 4 x - 1$
54645	Find g(f(x))	f(x)=6x^2-7 ; g(x)=2/x	$f (x) = 6 x^{2} - 7$ ; $g (x) = \frac{2}{x}$
54646	Find f(g(x))	f(x)=3x^2-7 ; g(x)=4/x	$f (x) = 3 x^{2} - 7$ ; $g (x) = \frac{4}{x}$
54647	Find f(g(x))	f(x)=x^3-3x^2 , g(x)=3x^2-1	$f (x) = x^{3} - 3 x^{2}$ , $g (x) = 3 x^{2} - 1$
54648	Find f(g(x))	f(x)=x^3 , g(x)=x^2+5x-6	$f (x) = x^{3}$ , $g (x) = x^{2} + 5 x - 6$
54649	Find f(g(x))	f(x)=2x+4 , g(x)=6x-1	$f (x) = 2 x + 4$ , $g (x) = 6 x - 1$
54650	Find f(g(x))	f(x)=x^2 , g(x)=5x-4	$f (x) = x^{2}$ , $g (x) = 5 x - 4$
54651	Find f(g(x))	f(x)=3x-5 g(x)=7-x^2	$f (x) = 3 x - 5$ $g (x) = 7 - x^{2}$
54652	Find f(g(x))	f(x)=x/10+3 , g(x)=2x-1	$f (x) = \frac{x}{10} + 3$ , $g (x) = 2 x - 1$
54653	Find g(f(x))	f(x)=x/6+5 , g(x)=2x-3	$f (x) = \frac{x}{6} + 5$ , $g (x) = 2 x - 3$
54654	Find g(f(x))	f(x)=3x-5 g(x)=7-x^2	$f (x) = 3 x - 5$ $g (x) = 7 - x^{2}$
54655	Find g(f(x))	f(x)=x^3 , g(x)=x^2+5x-6	$f (x) = x^{3}$ , $g (x) = x^{2} + 5 x - 6$
54656	Find g(f(x))	f(x) = square root of x , g(x) = seventh root of 7-x	$f (x) = \sqrt{x}$ , $g (x) = \sqrt[7]{7 - x}$
54657	Find g(f(x))	f(x)=2x+4 , g(x)=6x-1	$f (x) = 2 x + 4$ , $g (x) = 6 x - 1$
54658	Find g(f(x))	f(x)=5x+9 ; g(x)=4x-7	$f (x) = 5 x + 9$ ; $g (x) = 4 x - 7$
54659	Find g(f(x))	f(x)=2x^2-5 ; g(x)=4/x	$f (x) = 2 x^{2} - 5$ ; $g (x) = \frac{4}{x}$
54660	Find g(f(x))	f(x)=x^5 , g(x)=1/(3x+1)	$f (x) = x^{5}$ , $g (x) = \frac{1}{3 x + 1}$
54661	Find Where Undefined/Discontinuous	y=(x^2+4x-5)/(x^2+8x+15)	$y = \frac{(x^{2} + 4 x - 5)}{(x^{2} + 8 x + 15)}$
54662	Find Where Undefined/Discontinuous	y=1/(x-2)-3x	$y = \frac{1}{x - 2} - 3 x$
54663	Find f(g(z))	f(z)=z^8 , g(x)=3x^2+4	$f (z) = z^{8}$ , $g (x) = 3 x^{2} + 4$
54664	Find D(P(x))	P(x)=x^3-216 D(x)=x+6	$P (x) = x^{3} - 216$ $D (x) = x + 6$
54665	Find g(f(u))	f(u)=u^3 ; g(x)=3x^4+7	$f (u) = u^{3}$ ; $g (x) = 3 x^{4} + 7$
54666	Find P(C(x))	P(x)=20 C(x)=2x^2+450	$P (x) = 20$ $C (x) = 2 x^{2} + 450$
54667	Find g(f(z))	f(z)=z^8 , g(x)=3x^2+4	$f (z) = z^{8}$ , $g (x) = 3 x^{2} + 4$
54668	Find g(f(u))	f(u)=u^8 ; g(x)=6x^6+7	$f (u) = u^{8}$ ; $g (x) = 6 x^{6} + 7$
54669	Verify the Identity	(sec(theta)-1)(sec(theta)+1)=tan(theta)^2	$(\sec (θ) - 1) (\sec (θ) + 1) = \tan^{2} (θ)$
54670	Verify the Identity	cot(theta)(tan(theta)^2-sin(theta)^2)=tan(theta)sin(theta)^2	$\cot (θ (\tan^{2} (θ) - \sin^{2} (θ))) = \tan (θ) \sin^{2} (θ)$
54671	Verify the Identity	sec(x)=sec(x)tan(x)	$\sec (x) = \sec (x) \tan (x)$
54672	Verify the Identity	tan(theta)=(cos(theta))/(sin(theta))	$\tan (θ) = \frac{\cos (θ)}{\sin (θ)}$
54673	Verify the Identity	sin(pi+theta)=-sin(theta)	$\sin (π + θ) = - \sin (θ)$
54674	Verify the Identity	1/(1-sin(theta))+1/(1+sin(theta))=2sec(theta)^2	$\frac{1}{1 - \sin (θ)} + \frac{1}{1 + \sin (θ)} = 2 \sec^{2} (θ)$
54675	Verify the Identity	(sec(theta))/(cos(theta))-(tan(theta))/(cot(theta))=1	$\frac{\sec (θ)}{\cos (θ)} - \frac{\tan (θ)}{\cot (θ)} = 1$
54676	Verify the Identity	sin(theta)sec(theta)=tan(theta)	$\sin (θ) \sec (θ) = \tan (θ)$
54677	Verify the Identity	tan(pi-theta)=-tan(theta)	$\tan (π - θ) = - \tan (θ)$
54678	Verify the Identity	2sin(theta)-1=csc(theta)	$2 \sin (θ) - 1 = \csc (θ)$
54679	Verify the Identity	(sin(theta))/(tan(theta))=cos(theta)	$\frac{\sin (θ)}{\tan (θ)} = \cos (θ)$
54680	Find the Integral	integral of 1/(csc(2x)-cot(2x)) with respect to x	$\int \frac{1}{\csc (2 x) - \cot (2 x)} d x$
54681	Convert to Trigonometric Form	\|(3pi)/4\|	$\| \frac{3 π}{4} \|$
54682	Convert to Trigonometric Form	3-2i	$3 - 2 i$
54683	Find the Integral	(dy)/(y^3)	$\frac{d y}{y^{3}}$
54684	Find the Integral	6cos(2x)^3	$6 \cos^{3} (2 x)$
54685	Find the Integral	e^(-4t)	$e^{- 4 t}$
54686	Find the Integral	y^(3/2)	$y^{\frac{3}{2}}$
54687	Find the Integral	(theta+1)x^(-theta-2)	$(θ + 1) x^{- θ - 2}$
54688	Find the Integral	(dy)/(y-1)	$\frac{d y}{y - 1}$
54689	Find the Integral	-sin(t)	$- \sin (t)$
54690	Find the Integral	xe^xdx	$x e^{x} d x$
54691	Find the Integral	2e^(1/2x)	$2 e^{\frac{1}{2} x}$
54692	Find the Integral	integral of sin(x)^4 with respect to x	$\int \sin^{4} (x) d x$
54693	Find the Integral	15/x	$\frac{15}{x}$
54694	Find the Integral	natural log of x^2	$\ln (x^{2})$
54695	Find the Integral	sec(2x)tan(2x)	$\sec (2 x) \tan (2 x)$
54696	Find the Integral	1/pdP	$\frac{1}{p} d P$
54697	Find the Integral	integral of x^2e^(x^3) with respect to x	$\int x^{2} e^{x^{3}} d x$
54698	Find the Integral	1/(x^2 square root of 4-x^2)	$\frac{1}{x^{2} \sqrt{4 - x^{2}}}$
54699	Find the Integral	18/( square root of 9y+19)	$\frac{18}{\sqrt{9 y + 19}}$
54700	Find the Integral	sin(3x)dx	$\sin (3 x) d x$