Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
45401	Add	( square root of 3x+7)+( square root of 3x-7)	$(\sqrt{3 x + 7}) + (\sqrt{3 x - 7})$
45402	Add	( square root of x^2-16)+((x^2)/(x^2+1))	$(\sqrt{x^{2} - 16}) + (\frac{x^{2}}{x^{2} + 1})$
45403	Add	(6x)/(x^2+6x+9)+7/(x^2+5x+6)	$\frac{6 x}{x^{2} + 6 x + 9} + \frac{7}{x^{2} + 5 x + 6}$
45404	Evaluate Using the Given Value	3x-2y+17x-3y=1	$3 x - 2 y + 17 x - 3 y = 1$
45405	Evaluate Using the Given Value	(-10x+20)/(x^2-x-20)x=-3	$\frac{- 10 x + 20}{x^{2} - x - 20} x = - 3$
45406	Expand the Logarithmic Expression	log base 5 of (xy^4)^4	$\log_{5} ({(x y^{4})}^{4})$
45407	Expand the Logarithmic Expression	log base 6 of ninth root of (s^6t)/36	$\log_{6} (\sqrt[9]{\frac{s^{6} t}{36}})$
45408	Expand the Logarithmic Expression	log base 5 of 25x+5y	$\log_{5} (25 x + 5 y)$
45409	Expand the Logarithmic Expression	log base 5 of (4p)/(5k)	$\log_{5} (\frac{4 p}{5 k})$
45410	Expand the Logarithmic Expression	log base 5 of 125x+75y	$\log_{5} (125 x + 75 y)$
45411	Expand the Logarithmic Expression	log base 5 of 15x+20y	$\log_{5} (15 x + 20 y)$
45412	Expand the Logarithmic Expression	log base 4 of 6x^4	$\log_{4} (6 x^{4})$
45413	Expand the Logarithmic Expression	log base 3 of 18x+45y	$\log_{3} (18 x + 45 y)$
45414	Expand the Logarithmic Expression	log base 3 of (27x)^2	$\log_{3} ({(27 x)}^{2})$
45415	Expand the Logarithmic Expression	log base 3 of 12x^7	$\log_{3} (12 x^{7})$
45416	Expand the Logarithmic Expression	log base 3 of (9x^3y)/(z^2 square root of w)	$\log_{3} (\frac{9 x^{3} y}{z^{2} \sqrt{w}})$
45417	Expand the Logarithmic Expression	log base 4 of 8x	$\log_{4} (8 x)$
45418	Expand the Logarithmic Expression	log base 4 of (x^5)/(y^8)	$\log_{4} (\frac{x^{5}}{y^{8}})$
45419	Expand the Logarithmic Expression	log base 17 of ( cube root of 14)/(n^2m)	$\log_{17} (\frac{\sqrt[3]{14}}{n^{2} m})$
45420	Expand the Logarithmic Expression	log base 2 of 8x+12y	$\log_{2} (8 x + 12 y)$
45421	Expand the Logarithmic Expression	log base 2 of 5x^3	$\log_{2} (5 x^{3})$
45422	Expand the Logarithmic Expression	log base 2 of 3a^4	$\log_{2} (3 a^{4})$
45423	Expand the Logarithmic Expression	log base 2 of (x^6)/(x^5)	$\log_{2} (\frac{x^{6}}{x^{5}})$
45424	Expand the Logarithmic Expression	log of zx^2	$\log (z x^{2})$
45425	Expand the Logarithmic Expression	log of zy^2	$\log (z y^{2})$
45426	Expand the Logarithmic Expression	log of XY	$\log (X Y)$
45427	Expand the Logarithmic Expression	log base 7 of (x^2)/(y^2z^3)	$\log_{7} (\frac{x^{2}}{y^{2} z^{3}})$
45428	Expand the Logarithmic Expression	log base 8 of (4x+2)/( sixth root of 2-3x)	$\log_{8} (\frac{4 x + 2}{\sqrt[6]{2 - 3 x}})$
45429	Expand the Logarithmic Expression	log base 8 of x^(3/2)	$\log_{8} (x^{\frac{3}{2}})$
45430	Expand the Logarithmic Expression	log base 8 of 6 square root of xy	$\log_{8} (6 \sqrt{x y})$
45431	Expand the Logarithmic Expression	log base a of (x^9)/(yz^5)	$\log_{a} (\frac{x^{9}}{y z^{5}})$
45432	Expand the Logarithmic Expression	log base b of 14/(3b)	$\log_{b} (\frac{14}{3 b})$
45433	Expand the Logarithmic Expression	log base b of 4/c	$\log_{b} (\frac{4}{c})$
45434	Expand the Logarithmic Expression	log base b of (a^5c^2)/(d^6)	$\log_{b} (\frac{a^{5} c^{2}}{d^{6}})$
45435	Expand the Logarithmic Expression	log base b of ((mz^3)/n)^(3/5)	$\log_{b} ({(\frac{m z^{3}}{n})}^{\frac{3}{5}})$
45436	Expand the Logarithmic Expression	log base b of y^7z	$\log_{b} (y^{7} z)$
45437	Expand the Logarithmic Expression	log base b of (xy^5)/(z^4)	$\log_{b} (\frac{x y^{5}}{z^{4}})$
45438	Expand the Logarithmic Expression	5 log of (x^2 square root of z)/(9y^2)	$5 \log (\frac{x^{2} \sqrt{z}}{9 y^{2}})$
45439	Expand the Logarithmic Expression	natural log of 5/(6x^6y)	$\ln (\frac{5}{6 x^{6} y})$
45440	Expand the Logarithmic Expression	natural log of (x^3)/(y^6 square root of z^7)	$\ln (\frac{x^{3}}{y^{6} \sqrt{z^{7}}})$
45441	Expand the Logarithmic Expression	log of z^9y	$\log (z^{9} y)$
45442	Expand the Logarithmic Expression	log of 14x	$\log (14 x)$
45443	Expand the Logarithmic Expression	log of 3e	$\log (3 e)$
45444	Expand the Logarithmic Expression	log of x square root of z	$\log (x \sqrt{z})$
45445	Expand the Logarithmic Expression	log base 15 of (4 square root of x)/y	$\log_{15} (\frac{4 \sqrt{x}}{y})$
45446	Expand the Logarithmic Expression	log base 2 of 8/( square root of x+8)	$\log_{2} (\frac{8}{\sqrt{x + 8}})$
45447	Expand the Logarithmic Expression	log base 5 of 50x+75y	$\log_{5} (50 x + 75 y)$
45448	Find the Roots (Zeros)	f(x)=2x^3+3x^2-4x-6	$f (x) = 2 x^{3} + 3 x^{2} - 4 x - 6$
45449	Find the Roots (Zeros)	f(x)=2x^3+7x^2+2x-3	$f (x) = 2 x^{3} + 7 x^{2} + 2 x - 3$
45450	Find the Roots (Zeros)	f(x)=2x^3+7x^2+98x+343	$f (x) = 2 x^{3} + 7 x^{2} + 98 x + 343$
45451	Find the Roots (Zeros)	f(x)=(x+2)^2-25	$f (x) = {(x + 2)}^{2} - 25$
45452	Find the Roots (Zeros)	f(x) = log base 2 of 2x-3	$f (x) = \log_{2} (2 x - 3)$
45453	Find the Roots (Zeros)	f(x) = square root of 3csc(x)+2	$f (x) = \sqrt{3} \csc (x) + 2$
45454	Find the Roots (Zeros)	f(x) = square root of 4x+3	$f (x) = \sqrt{4 x + 3}$
45455	Find the Roots (Zeros)	f(x)=1/2cos(2x)	$f (x) = \frac{1}{2} \cos (2 x)$
45456	Find the Roots (Zeros)	f(x)=24x^3-10x^2-7x+2	$f (x) = 24 x^{3} - 10 x^{2} - 7 x + 2$
45457	Find the Roots (Zeros)	f(x)=3x^3-12x^2+6x	$f (x) = 3 x^{3} - 12 x^{2} + 6 x$
45458	Find the Roots (Zeros)	f(x)=7x^4-6x^3+174x^2-150x-25	$f (x) = 7 x^{4} - 6 x^{3} + 174 x^{2} - 150 x - 25$
45459	Find the Roots (Zeros)	F(x)=4x^2+5x-21	$F (x) = 4 x^{2} + 5 x - 21$
45460	Find the Roots (Zeros)	f(x)=8x^3-3x^2+5x+15	$f (x) = 8 x^{3} - 3 x^{2} + 5 x + 15$
45461	Find the Roots (Zeros)	f(x)=8x^4-22x^3-89x^2-11x+30	$f (x) = 8 x^{4} - 22 x^{3} - 89 x^{2} - 11 x + 30$
45462	Find the Roots (Zeros)	f(x)=x^2-3x-18	$f (x) = x^{2} - 3 x - 18$
45463	Find the Roots (Zeros)	f(x)=x^2-10x+34	$f (x) = x^{2} - 10 x + 34$
45464	Find the Roots (Zeros)	f(x)=x^2+x-20	$f (x) = x^{2} + x - 20$
45465	Find the Roots (Zeros)	p(x)=x^3-3x^2-5x+39	$p (x) = x^{3} - 3 x^{2} - 5 x + 39$
45466	Find the Roots (Zeros)	p(x)=x^3-5x^2+11x-15	$p (x) = x^{3} - 5 x^{2} + 11 x - 15$
45467	Find the Roots (Zeros)	f(x)=x^5+x^3-42x	$f (x) = x^{5} + x^{3} - 42 x$
45468	Find the Roots (Zeros)	f(x)=x^4-8x^3+42x^2-8x+41	$f (x) = x^{4} - 8 x^{3} + 42 x^{2} - 8 x + 41$
45469	Find the Roots (Zeros)	h(x)=7x^3+9x^2-12x-4	$h (x) = 7 x^{3} + 9 x^{2} - 12 x - 4$
45470	Find the Roots (Zeros)	g(x)=x^3+6x^2-3x-18	$g (x) = x^{3} + 6 x^{2} - 3 x - 18$
45471	Find the Roots (Zeros)	f(x)=x^3-8x^2+9x+18	$f (x) = x^{3} - 8 x^{2} + 9 x + 18$
45472	Find the Roots (Zeros)	f(x)=x^3-7x^2+4x+12	$f (x) = x^{3} - 7 x^{2} + 4 x + 12$
45473	Find the Roots (Zeros)	f(x)=x^3-x^2+9x-9	$f (x) = x^{3} - x^{2} + 9 x - 9$
45474	Find the Roots (Zeros)	f(x)=x^4-3x^3-6x^2-12x-40	$f (x) = x^{4} - 3 x^{3} - 6 x^{2} - 12 x - 40$
45475	Find the Roots (Zeros)	f(x)=x^4-6x^3+50x^2+122x+65	$f (x) = x^{4} - 6 x^{3} + 50 x^{2} + 122 x + 65$
45476	Find the Roots (Zeros)	f(x)=x^4-4x^3-10x^2-20x-75	$f (x) = x^{4} - 4 x^{3} - 10 x^{2} - 20 x - 75$
45477	Find the Roots (Zeros)	f(x)=x^4-4x^3-9x^2+36x	$f (x) = x^{4} - 4 x^{3} - 9 x^{2} + 36 x$
45478	Find the Roots (Zeros)	f(x)=x^4+25x^2+144	$f (x) = x^{4} + 25 x^{2} + 144$
45479	Find the Roots (Zeros)	f(x)=x^4-3x^3-3x^2+7x+3	$f (x) = x^{4} - 3 x^{3} - 3 x^{2} + 7 x + 3$
45480	Find the Roots (Zeros)	f(x)=x^3-11x^2+40x-50	$f (x) = x^{3} - 11 x^{2} + 40 x - 50$
45481	Find the Local Maxima and Minima	f(x)=x^3-2.4x+3	$f (x) = x^{3} - 2.4 x + 3$
45482	Find the Local Maxima and Minima	g(x)=x^3+5x^2-17x-21	$g (x) = x^{3} + 5 x^{2} - 17 x - 21$
45483	Solve by Completing the Square	3x^2-12x+6=0	$3 x^{2} - 12 x + 6 = 0$
45484	Solve by Completing the Square	25x^2-40x-34=0	$25 x^{2} - 40 x - 34 = 0$
45485	Identify the Conic	x^2-4y^2-6x+16y-21=0	$x^{2} - 4 y^{2} - 6 x + 16 y - 21 = 0$
45486	Identify the Conic	x^2+9y^2+10x-18y+25=0	$x^{2} + 9 y^{2} + 10 x - 18 y + 25 = 0$
45487	Identify the Conic	x^2+4x+y^2-2y-49=0	$x^{2} + 4 x + y^{2} - 2 y - 49 = 0$
45488	Identify the Conic	((x-1)^2)/4+((y-5)^2)/81=1	$\frac{{(x - 1)}^{2}}{4} + \frac{{(y - 5)}^{2}}{81} = 1$
45489	Evaluate from the Left	limit as x approaches 2 from the right of f(x)	$lim_{x \to 2} f (x)$
45490	Convert to Degrees, Minutes, and Seconds	12.22 degrees	$12.22 °$
45491	Identify the Conic	3x^2-5xy-2y^2+4x-3y=12	$3 x^{2} - 5 x y - 2 y^{2} + 4 x - 3 y = 12$
45492	Identify the Conic	6x^2-8xy-2y^2+6=0	$6 x^{2} - 8 x y - 2 y^{2} + 6 = 0$
45493	Identify the Conic	25y^2-144x^2+150y-576x-3951=0	$25 y^{2} - 144 x^{2} + 150 y - 576 x - 3951 = 0$
45494	Identify the Conic	2x^2+4xy+4y^2=0	$2 x^{2} + 4 x y + 4 y^{2} = 0$
45495	Identify the Conic	13x^2+6 square root of 3xy+7y^2-16=0	$13 x^{2} + 6 \sqrt{3 x y} + 7 y^{2} - 16 = 0$
45496	Identify the Conic	(x-3)^2=8(y+1)	${(x - 3)}^{2} = 8 (y + 1)$
45497	Identify the Conic	(x^2)/4+(y^2)/64=1	$\frac{x^{2}}{4} + \frac{y^{2}}{64} = 1$
45498	Expand Using Sum/Difference Formulas	sin(4theta)sin(2theta)	$\sin (4 θ) \sin (2 θ)$
45499	Expand Using Sum/Difference Formulas	10cos(5x)sin(10x)	$10 \cos (5 x) \sin (10 x)$
45500	Expand Using Sum/Difference Formulas	sin(6x)sin(4x)	$\sin (6 x) \sin (4 x)$