Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
23801	Simplify/Condense	log base 3 of ( square root of x^2y)/( cube root of xy)	$\log_{3} (\frac{\sqrt{x^{2} y}}{\sqrt[3]{x y}})$
23802	Simplify/Condense	log base 3 of ( cube root of 5)/(r^2q)	$\log_{3} (\frac{\sqrt[3]{5}}{r^{2} q})$
23803	Find the Directrix	y^2=-12x	$y^{2} = - 12 x$
23804	Simplify/Condense	- log base 3 of 1/7	$- \log_{3} (\frac{1}{7})$
23805	Find the Directrix	y^2=-20x	$y^{2} = - 20 x$
23806	Identify the Conic	y^2+8y-10y-34=0	$y^{2} + 8 y - 10 y - 34 = 0$
23807	Write in Standard Form	r=2/(1+cos(theta))	$r = \frac{2}{1 + \cos (θ)}$
23808	Simplify/Condense	log base 2 of x+7+1/2* log base 2 of x	$\log_{2} (x + 7) + \frac{1}{2} \cdot \log_{2} (x)$
23809	Simplify/Condense	log base 2 of x+7+1/7* log base 2 of x	$\log_{2} (x + 7) + \frac{1}{7} \cdot \log_{2} (x)$
23810	Simplify/Condense	log base 25 of 1/25	$\log_{25} (\frac{1}{25})$
23811	Simplify/Condense	log base 25 of 5+ log base 25 of 3125	$\log_{25} (5) + \log_{25} (3125)$
23812	Simplify/Condense	log base 25 of 75+ log base 25 of 35- log base 25 of 21	$\log_{25} (75) + \log_{25} (35) - \log_{25} (21)$
23813	Simplify/Condense	log base 27 of 4/3	$\log_{27} (\frac{4}{3})$
23814	Graph	x=y^2-25	$x = y^{2} - 25$
23815	Simplify/Condense	log base 3.1 of x	$\log_{3.1} (x)$
23816	Simplify/Condense	log base 3.14 of 57	$\log_{3.14} (57)$
23817	Simplify/Condense	log base 3 of ( cube root of x)/81	$\log_{3} (\frac{\sqrt[3]{x}}{81})$
23818	Simplify/Condense	log base 2 of sin(pi/4)	$\log_{2} (\sin (\frac{π}{4}))$
23819	Graph	f(x) = square root of 4+x,x<0; square root of 4-x,x>=0	$f (x) = {\begin{cases} \sqrt{4 + x}, x < 0 \\ \sqrt{4 - x}, x \geq 0 \end{cases}$
23820	Simplify/Condense	log base 15 of 10	$\log_{15} (10)$
23821	Graph	(y^2)/6-(x^2)/12=1	$\frac{y^{2}}{6} - \frac{x^{2}}{12} = 1$
23822	Simplify/Condense	log base 16 of 1/64	$\log_{16} (\frac{1}{64})$
23823	Simplify/Condense	log base 16 of x^8+ log base 8 of y^6- log base 4 of w^4	$\log_{16} (x^{8}) + \log_{8} (y^{6}) - \log_{4} (w^{4})$
23824	Simplify/Condense	log base 17 of ( square root of 15)/(q^2p)	$\log_{17} (\frac{\sqrt{15}}{q^{2} p})$
23825	Simplify/Condense	log base 17 of 6/13	$\log_{17} (\frac{6}{13})$
23826	Simplify/Condense	log base 17 of 7/16	$\log_{17} (\frac{7}{16})$
23827	Simplify/Condense	log base 2 of 0.5(x+3)^6	$\log_{2} (0.5 {(x + 3)}^{6})$
23828	Simplify/Condense	log base 11 of 3+2 log base 11 of 5	$\log_{11} (3) + 2 \log_{11} (5)$
23829	Simplify/Condense	log base 11 of 5	$\log_{11} (5)$
23830	Simplify/Condense	log base 12 of 8+ log base 12 of 2+ log base 12 of 9	$\log_{12} (8) + \log_{12} (2) + \log_{12} (9)$
23831	Simplify/Condense	log base 13 of 1/( square root of 13)	$\log_{13} (\frac{1}{\sqrt{13}})$
23832	Simplify/Condense	log base 13 of 13/y	$\log_{13} (\frac{13}{y})$
23833	Simplify/Condense	log base 14 of square root of 14	$\log_{14} (\sqrt{14})$
23834	Simplify/Condense	3^(2 log base 3 of 4)+ log base 3 of 2	$3^{2 \log_{3} (4)} + \log_{3} (2)$
23835	Simplify/Condense	3/2* natural log of 4x^10-2/5* natural log of 2y^15	$\frac{3}{2} \cdot \ln (4 x^{10}) - \frac{2}{5} \cdot \ln (2 y^{15})$
23836	Simplify/Condense	3/2* natural log of 4x^8-2/5* natural log of 2y^15	$\frac{3}{2} \cdot \ln (4 x^{8}) - \frac{2}{5} \cdot \ln (2 y^{15})$
23837	Simplify/Condense	3/2* natural log of x-y-2 natural log of x^(2+y^2)	$\frac{3}{2} \cdot \ln (x - y) - 2 \ln (x^{2 + y^{2}})$
23838	Simplify/Condense	log of fourth root of 1/100000	$\log (\sqrt[4]{\frac{1}{100000}})$
23839	Simplify/Condense	log of x^2-9-3 log of x+3+6 log of x	$\log (x^{2} - 9) - 3 \log (x + 3) + 6 \log (x)$
23840	Convert from Radians to Degrees	0.86602540	$0.8660254$
23841	Simplify/Condense	log base 0.03 of 6	$\log_{0.03} (6)$
23842	Simplify/Condense	log base 1/2 of 128	$\log_{\frac{1}{2}} (128)$
23843	Find the Center and Radius	x^2-12x+y^2+10y+12=0	$x^{2} - 12 x + y^{2} + 10 y + 12 = 0$
23844	Simplify/Condense	log of 2.3^4	$\log ({2.3}^{4})$
23845	Simplify/Condense	log base 2 of 67/(4y)	$\log_{2} (\frac{67}{4 y})$
23846	Evaluate	( log of 81/16)/( log of 2/3)	$\frac{\log (\frac{81}{16})}{\log (\frac{2}{3})}$
23847	Simplify/Condense	log base 2 of 1/25	$\log_{2} (\frac{1}{25})$
23848	Simplify/Condense	log base 100 of 22	$\log_{100} (22)$
23849	Simplify	y/( cube root of 5)	$\frac{y}{\sqrt[3]{5}}$
23850	Simplify/Condense	log base 2 of (xy)/(tqr)	$\log_{2} (\frac{x y}{t q r})$
23851	Simplify/Condense	log base 2 of 10- log base 2 of 20	$\log_{2} (10) - \log_{2} (20)$
23852	Simplify/Condense	log base 2 of 10- log base 2 of 35+ log base 2 of 28	$\log_{2} (10) - \log_{2} (35) + \log_{2} (28)$
23853	Simplify/Condense	log base 2 of 12-2 log base 2 of 6+ log base 2 of 2	$\log_{2} (12) - 2 \log_{2} (6) + \log_{2} (2)$
23854	Simplify/Condense	log base 2 of cube root of (x^2)/(y square root of 2)	$\log_{2} (\sqrt[3]{\frac{x^{2}}{y \sqrt{2}}})$
23855	Simplify/Condense	log base 2 of cube root of 16	$\log_{2} (\sqrt[3]{16})$
23856	Simplify/Condense	log base 2 of cube root of 4	$\log_{2} (\sqrt[3]{4})$
23857	Simplify/Condense	log base 2 of 16^(1/5)	$\log_{2} (16^{\frac{1}{5}})$
23858	Simplify/Condense	log base 2 of 64x	$\log_{2} (64 x)$
23859	Simplify/Condense	log base 2 of 72-1/2*( log base 2 of 3+ log base 2 of 27)	$\log_{2} (72) - \frac{1}{2} \cdot (\log_{2} (3) + \log_{2} (27))$
23860	Simplify/Condense	log base 2 of 5x^2y^3- log base 2 of 20x^4y+ log base 2 of 2xy^6	$\log_{2} (5 x^{2} y^{3}) - \log_{2} (20 x^{4} y) + \log_{2} (2 x y^{6})$
23861	Simplify/Condense	log base 2 of 4(x^2-4)	$\log_{2} (4) (x^{2} - 4)$
23862	Simplify/Condense	log base 2 of 12*14	$\log_{2} (12 \cdot 14)$
23863	Simplify/Condense	log base 2 of 125- log base 2 of 5+ log base 2 of 3	$\log_{2} (125) - \log_{2} (5 + \log_{2} (3))$
23864	Verify the Identity	1+cos(8x)=2cos(4x)^2	$1 + \cos (8 x) = 2 \cos^{2} (4 x)$
23865	Simplify/Condense	2 log base 3 of x+5- log base 3 of x-2- log base 3 of x-1	$2 \log_{3} (x + 5) - \log_{3} (x - 2) - \log_{3} (x - 1)$
23866	Simplify/Condense	2 log base 3 of x+8- log base 3 of x-17- log base 3 of x-9	$2 \log_{3} (x + 8) - \log_{3} (x - 17) - \log_{3} (x - 9)$
23867	Simplify/Condense	2 log base 4 of x^2-4 log base 4 of x^3+2 log base 3 of x	$2 \log_{4} (x^{2}) - 4 \log_{4} (x^{3}) + 2 \log_{3} (x)$
23868	Simplify/Condense	2 log base 4 of x^3-4 log base 4 of x^-5+3 log base 4 of x	$2 \log_{4} (x^{3}) - 4 \log_{4} (x^{- 5}) + 3 \log_{4} (x)$
23869	Simplify/Condense	2 log base 4 of x+3 log base 4 of z	$2 \log_{4} (x + 3) \log_{4} (z)$
23870	Simplify/Condense	2 log base 5 of square root of 3x-8	$2 \log_{5} (\sqrt{3 x - 8})$
23871	Simplify/Condense	2 log base 5 of x^3+3 log base 5 of x-6 log base 5 of x^(-(2))	$2 \log_{5} (x^{3}) + 3 \log_{5} (x) - 6 \log_{5} (x^{- (2)})$
23872	Simplify/Condense	2 log base 5 of u+3 log base 5 of v	$2 \log_{5} (u) + 3 \log_{5} (v)$
23873	Simplify/Condense	2 log base 7 of 11-6 log base 7 of 5	$2 \log_{7} (11) - 6 \log_{7} (5)$
23874	Simplify/Condense	2 log base 7 of 12	$2 \log_{7} (12)$
23875	Simplify/Condense	2 log base 7 of x- log base 7 of y+1/2* log base 7 of z	$2 \log_{7} (x) - \log_{7} (y) + \frac{1}{2} \cdot \log_{7} (z)$
23876	Simplify/Condense	2 log base 8 of 7+ log base 8 of 4- log base 8 of 2	$2 \log_{8} (7) + \log_{8} (4) - \log_{8} (2)$
23877	Simplify/Condense	2 log base 8 of y+4( log base 8 of w-5 log base 8 of z)	$2 \log_{8} (y + 4) (\log_{8} (w) - 5 \log_{8} (z))$
23878	Simplify/Condense	2 log base a of 9x^4-1/8* log base a of 8x+3	$2 \log_{a} (9 x^{4}) - \frac{1}{8} \cdot \log_{a} (8 x + 3)$
23879	Simplify/Condense	2 log base a of z+1+ log base a of 3z+2	$2 \log_{a} (z + 1) + \log_{a} (3 z + 2)$
23880	Simplify/Condense	2 log base b of m-6/5* log base b of n+1/3* log base b of j-6 log base b of k	$2 \log_{b} (m) - \frac{6}{5} \cdot \log_{b} (n) + \frac{1}{3} \cdot \log_{b} (j) - 6 \log_{b} (k)$
23881	Simplify/Condense	2 log base b of t-4/5 log base b of s+1/3* log base b of v-4	$2 \log_{b} (t - \frac{4}{5}) \log_{b} (s) + \frac{1}{3} \cdot \log_{b} (v - 4)$
23882	Simplify/Condense	-2+( natural log of 339)/( natural log of 2)	$- 2 + \frac{\ln (339)}{\ln (2)}$
23883	Simplify/Condense	2+2 natural log of x+4 natural log of x^2+10	$2 + 2 \ln (x) + 4 \ln (x^{2} + 10)$
23884	Simplify/Condense	20 log base 7 of y+12 log base 7 of x-4 log base 7 of z	$20 \log_{7} (y) + 12 \log_{7} (x) - 4 \log_{7} (z)$
23885	Solve for x	e^(x+2)=4	$e^{x + 2} = 4$
23886	Simplify/Condense	2e^(-4 natural log of x)	$2 e^{- 4 \ln (x)}$
23887	Simplify/Condense	2 log of (2)^7	$2 \log ({(2)}^{7})$
23888	Simplify/Condense	2 log of (3)^5+ log of (3)^2	$2 \log ({(3)}^{5}) + \log ({(3)}^{2})$
23889	Simplify/Condense	2 log base 2 of a-(4 log base 2 of b+3 log base 2 of c)	$2 \log_{2} (a) - (4 \log_{2} (b) + 3 \log_{2} (c))$
23890	Simplify/Condense	2 log base 2 of x+ log base 2 of 12- log base 2 of y	$2 \log_{2} (x) + \log_{2} (12) - \log_{2} (y)$
23891	Simplify/Condense	2 log base 2 of x-5	$2 \log_{2} (x - 5)$
23892	Simplify/Condense	2 log base 2 of z-5-4 log base 2 of z+7	$2 \log_{2} (z - 5) - 4 \log_{2} (z) + 7$
23893	Simplify/Condense	2 log base 3 of square root of 7x-3- log base 3 of 5/6+ log base 3 of 5	$2 \log_{3} (\sqrt{7 x - 3}) - \log_{3} (\frac{5}{6}) + \log_{3} (5)$
23894	Simplify/Condense	2 log base 3 of 10- log base 3 of 4	$2 \log_{3} (10) - \log_{3} (4)$
23895	Simplify/Condense	2 log base 3 of 4+ log base 3 of 2	$2 \log_{3} (4) + \log_{3} (2)$
23896	Simplify	cos(2kpi-theta)(-sin(2kpi-theta))	$\cos (2 k π - θ) (- \sin (2 k π - θ))$
23897	Simplify/Condense	log base b of fifth root of ((x-1)^2)/((y+3)^4(x-2))	$\log_{b} (\sqrt[5]{\frac{{(x - 1)}^{2}}{{(y + 3)}^{4} (x - 2)}})$
23898	Simplify/Condense	18 log base 3 of cube root of x+ log base 3 of 18x^4- log base 3 of 18	$18 \log_{3} (\sqrt[3]{x}) + \log_{3} (18 x^{4}) - \log_{3} (18)$
23899	Simplify/Condense	18 natural log of x+6 natural log of y	$18 \ln (x) + 6 \ln (y)$
23900	Simplify/Condense	2( log base 5 of x+ log base 5 of y)	$2 (\log_{5} (x) + \log_{5} (y))$