Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
23901	Simplify/Condense	2( log base 5 of x+3 log base 5 of y-5 log base 5 of z)	$2 (\log_{5} (x) + 3 \log_{5} (y) - 5 \log_{5} (z))$
23902	Simplify/Condense	2( log base 7 of z-5 log base 7 of w)+ log base 7 of x	$2 (\log_{7} (z - 5 \log_{7} (w))) + \log_{7} (x)$
23903	Simplify/Condense	2( log base 8 of x-3 log base 8 of w)+3 log base 8 of y	$2 (\log_{8} (x) - 3 \log_{8} (w)) + 3 \log_{8} (y)$
23904	Simplify/Condense	2( log base 8 of z-4 log base 8 of x)+2 log base 8 of y	$2 (\log_{8} (z) - 4 \log_{8} (x)) + 2 \log_{8} (y)$
23905	Simplify/Condense	2( log of 15- log of 5)+1/2* log of 1/25	$2 (\log (15) - \log (5)) + \frac{1}{2} \cdot \log (\frac{1}{25})$
23906	Find the Domain	10-x	$10 - x$
23907	Simplify/Condense	log base p of 78	$\log_{p} (78)$
23908	Simplify/Condense	log base t of L+ log base t of a	$\log_{t} (L) + \log_{t} (a)$
23909	Simplify/Condense	log base x of 3/10	$\log_{x} (\frac{3}{10})$
23910	Simplify/Condense	log base x of 16	$\log_{x} (16)$
23911	Simplify/Condense	log base x of 70+ log base x of 43	$\log_{x} (70) + \log_{x} (43)$
23912	Simplify/Condense	square root of natural log of 1-x+2	$\sqrt{\ln (1 - x) + 2}$
23913	Simplify/Condense	square root of log of 87- log of 89	$\sqrt{\log (8) \cdot 7} - \log (8) \cdot 9$
23914	Simplify/Condense	square root of x-4- log base 8 of 13-x	$\sqrt{x - 4} - \log_{8} (13 - x)$
23915	Simplify/Condense	1.04-e(0.38 natural log of 4.4-0.54)	$1.04 - e (0.38 \ln (4.4) - 0.54)$
23916	Simplify/Condense	1+ log base 3 of 59049	$1 + \log_{3} (59049)$
23917	Simplify/Condense	-1+100 log of square root of 2.09	$- 1 + 100 \log (\sqrt{2.09})$
23918	Write in Standard Form	2x^2+2y^2+6x-8y+12=0	$2 x^{2} + 2 y^{2} + 6 x - 8 y + 12 = 0$
23919	Simplify/Condense	10 log base 8 of fifth root of y	$10 \log_{8} (\sqrt[5]{y})$
23920	Simplify/Condense	10000e^((( natural log of 2)/21)*60)	$10000 e^{(\frac{\ln (2)}{21}) \cdot 60}$
23921	Simplify/Condense	11+ log of 10x+21-1	$11 + \log (10 x + 21) - 1$
23922	Simplify/Condense	-11052+5742 natural log of 29	$- 11052 + 5742 \ln (29)$
23923	Simplify/Condense	112 natural log of 0.121x+2011	$112 \ln (0.121 x) + 2011$
23924	Find the Foci	4x^2+9y^2=36	$4 x^{2} + 9 y^{2} = 36$
23925	Simplify/Condense	log base c of x^4y^3z	$\log_{c} (x^{4} y^{3} z)$
23926	Simplify/Condense	log base c of 7-2 log base c of 4+1/4* log base c of 81	$\log_{c} (7) - 2 \log_{c} (4) + \frac{1}{4} \cdot \log_{c} (81)$
23927	Simplify/Condense	log base c of m+ log base c of n	$\log_{c} (m) + \log_{c} (n)$
23928	Simplify/Condense	log base f of square root of (xy^7)/(z^5)	$\log_{f} (\sqrt{\frac{x y^{7}}{z^{5}}})$
23929	Find the Domain and Range	2/(x^2-2x-3)	$\frac{2}{x^{2} - 2 x - 3}$
23930	Simplify/Condense	log base n of -10	$\log_{n} (- 10)$
23931	Simplify/Condense	log base 6 of 71	$\log_{6} (71)$
23932	Find the Standard Form of the Parabola	x^2-6x-6y-21=0	$x^{2} - 6 x - 6 y - 21 = 0$
23933	Simplify/Condense	log base 7 of 30	$\log_{7} (30)$
23934	Graph	y=3sin(1/3x)	$y = 3 \sin (\frac{1}{3} x)$
23935	Simplify/Condense	log base 7 of 5+ log base 7 of 8	$\log_{7} (5) + \log_{7} (8)$
23936	Simplify/Condense	log base 7 of 8- log base 7 of z	$\log_{7} (8) - \log_{7} (z)$
23937	Simplify/Condense	log base 7 of 94	$\log_{7} (94)$
23938	Simplify/Condense	3 log base 6 of x-2-( log base 6 of y+4 log base 6 of z)	$3 \log_{6} (x - 2) - (\log_{6} (y) + 4 \log_{6} (z))$
23939	Simplify/Condense	3 log base 7 of 4-5 log base 7 of m	$3 \log_{7} (4 - 5 \log_{7} (m))$
23940	Simplify/Condense	3 log base 7 of 5+(4 log base 7 of y-6-5 log base 7 of y)	$3 \log_{7} (5) + (4 \log_{7} (y - 6) - 5 \log_{7} (y))$
23941	Simplify/Condense	3 log base 7 of x+1/3* log base 7 of y	$3 \log_{7} (x) + \frac{1}{3} \cdot \log_{7} (y)$
23942	Simplify/Condense	-3 log base 8 of 2	$- 3 \log_{8} (2)$
23943	Simplify/Condense	3 log base 8 of x-1/3* log base 8 of z+7 log base 8 of w	$3 \log_{8} (x) - \frac{1}{3} \cdot \log_{8} (z) + 7 \log_{8} (w)$
23944	Simplify/Condense	3 log base a of 2+9 log base a of 9	$3 \log_{a} (2) + 9 \log_{a} (9)$
23945	Simplify/Condense	3 log base a of 5x^8-1/8* log base a of 3x+2	$3 \log_{a} (5 x^{8}) - \frac{1}{8} \cdot \log_{a} (3 x + 2)$
23946	Simplify/Condense	3 log base a of 6x^5-1/8* log base a of 3x+17	$3 \log_{a} (6 x^{5}) - \frac{1}{8} \cdot \log_{a} (3 x + 17)$
23947	Simplify/Condense	3 log base a of 6x^7-1/5* log base a of 4x+3	$3 \log_{a} (6 x^{7}) - \frac{1}{5} \cdot \log_{a} (4 x + 3)$
23948	Simplify/Condense	3 log base a of 8x^8-1/5* log base a of 8x+17	$3 \log_{a} (8 x^{8}) - \frac{1}{5} \cdot \log_{a} (8 x + 17)$
23949	Graph	f(x)=4x^2+3x+2	$f (x) = 4 x^{2} + 3 x + 2$
23950	Simplify/Condense	3 log base b of y-4 log base b of z+3 log base b of x	$3 \log_{b} (y - 4 \log_{b} (z)) + 3 \log_{b} (x)$
23951	Simplify/Condense	3 log base b of z+4( log base b of w-2 log base b of y)	$3 \log_{b} (z) + 4 (\log_{b} (w) - 2 \log_{b} (y))$
23952	Graph	f(x)=5cos(x)	$f (x) = 5 \cos (x)$
23953	Simplify/Condense	3 log base p of t+1/2* log base p of x-3/2* log base p of r-3 log base p of a	$3 \log_{p} (t) + \frac{1}{2} \cdot \log_{p} (x) - \frac{3}{2} \cdot \log_{p} (r) - 3 \log_{p} (a)$
23954	Graph	f(x)=5sin(x)	$f (x) = 5 \sin (x)$
23955	Simplify/Condense	3+8 natural log of 2	$3 + 8 \ln (2)$
23956	Simplify/Condense	3000e natural log of 7/(6/2)*12	$3000$ eln $(\frac{7}{\frac{6}{2}}) \cdot 12$
23957	Simplify/Condense	3 natural log of x^2- natural log of square root of x	$3 \ln (x^{2}) - \ln (\sqrt{x})$
23958	Simplify/Condense	3 natural log of x^3y+2 natural log of yz^3	$3 \ln (x^{3} y) + 2 \ln (y z^{3})$
23959	Simplify/Condense	3( log of 7- log of 3-3 log of x+1/2* log of y)	$3 (\log (7) - \log (3) - 3 \log (x) + \frac{1}{2} \cdot \log (y))$
23960	Simplify/Condense	3 log of (3)^(2x-2)+4 log of (3)^(4x-7)	$3 \log ({(3)}^{2 x - 2}) + 4 \log ({(3)}^{4 x - 7})$
23961	Simplify/Condense	3 log of x+ log of y	$3 \log (x) + \log (y)$
23962	Graph	r=4+cos(theta)	$r = 4 + \cos (θ)$
23963	Simplify/Condense	3 log base 2 of 3-1/2 log base 2 of 9-2 log base 2 of 6	$3 \log_{2} (3 - \frac{1}{2}) \log_{2} (9) - 2 \log_{2} (6)$
23964	Simplify/Condense	3 log base 2 of x- log base 2 of 2y+3	$3 \log_{2} (x) - \log_{2} (2 y) + 3$
23965	Simplify/Condense	3 log base 2 of x-2 log base 2 of z+ log base 2 of y-5 log base 2 of w	$3 \log_{2} (x) - 2 \log_{2} (z) + \log_{2} (y) - 5 \log_{2} (w)$
23966	Simplify/Condense	3 log base 2 of x+6- log base 2 of x-13- log base 2 of x-17	$3 \log_{2} (x + 6) - \log_{2} (x - 13) - \log_{2} (x - 17)$
23967	Simplify/Condense	3 log base 2 of x+7- log base 2 of x-15- log base 2 of x-3	$3 \log_{2} (x + 7) - \log_{2} (x - 15) - \log_{2} (x - 3)$
23968	Simplify/Condense	3 log base 2 of x+9- log base 2 of x-9- log base 2 of x-8	$3 \log_{2} (x + 9) - \log_{2} (x - 9) - \log_{2} (x - 8)$
23969	Simplify/Condense	3 log base 3 of 3- log base 3 of 3	$3 \log_{3} (3) - \log_{3} (3)$
23970	Simplify/Condense	3 log base 3 of r-2 log base 3 of p	$3 \log_{3} (r) - 2 \log_{3} (p)$
23971	Simplify/Condense	3 log base 3 of y-3 log base 3 of z+3 log base 3 of x	$3 \log_{3} (y - 3 \log_{3} (z)) + 3 \log_{3} (x)$
23972	Simplify/Condense	3 log base 4 of x^2+5 log base 4 of y	$3 \log_{4} (x^{2}) + 5 \log_{4} (y)$
23973	Simplify/Condense	3 log base 4 of 6x-5-4 log base 4 of 7x+1	$3 \log_{4} (6 x - 5) - 4 \log_{4} (7 x + 1)$
23974	Simplify/Condense	3 log base 4 of A+3 log base 4 of B-2 log base 4 of C	$3 \log_{4} (A) + 3 \log_{4} (B) - 2 \log_{4} (C)$
23975	Simplify/Condense	3 log base 4 of x-1/2	$3 \log_{4} (x - \frac{1}{2})$
23976	Simplify/Condense	3 log base 5 of 2- log base 5 of 3	$3 \log_{5} (2) - \log_{5} (3)$
23977	Simplify/Condense	3 log base 5 of 2+5 log base 5 of x-1/5* log base 5 of y	$3 \log_{5} (2) + 5 \log_{5} (x) - \frac{1}{5} \cdot \log_{5} (y)$
23978	Simplify/Condense	3 log base 5 of 2x+1-2 log base 5 of 2x-1+1/2* log base 5 of x	$3 \log_{5} (2 x + 1) - 2 \log_{5} (2 x - 1) + \frac{1}{2} \cdot \log_{5} (x)$
23979	Simplify/Condense	3 log base 5 of 6x+1+1/2* log base 5 of x+5	$3 \log_{5} (6 x + 1) + \frac{1}{2} \cdot \log_{5} (x + 5)$
23980	Simplify/Condense	3 log base 5 of u+4 log base 5 of 5	$3 \log_{5} (u) + 4 \log_{5} (5)$
23981	Simplify/Condense	3 log base 5 of u+8 log base 5 of v	$3 \log_{5} (u) + 8 \log_{5} (v)$
23982	Simplify/Condense	3 log base 5 of x+1/2* log base 5 of y-2 log base 5 of 2	$3 \log_{5} (x) + \frac{1}{2} \cdot \log_{5} (y) - 2 \log_{5} (2)$
23983	Find the Quadrant of the Angle	202 degrees	$202 °$
23984	Simplify/Condense	3 log base 5 of x+4 log base 5 of y- log base 5 of z	$3 \log_{5} (x) + 4 \log_{5} (y) - \log_{5} (z)$
23985	Simplify/Condense	3 log base 5 of x+3/2 log base 5 of y- log base 5 of 5z	$3 \log_{5} (x + \frac{3}{2}) \log_{5} (y) - \log_{5} (5 z)$
23986	Simplify/Condense	3 log base 6 of u+4 log base 6 of v	$3 \log_{6} (u) + 4 \log_{6} (v)$
23987	Simplify/Condense	2 natural log of a+2 natural log of b- natural log of a	$2 \ln (a) + 2 \ln (b) - \ln (a)$
23988	Simplify/Condense	2 natural log of a+3 natural log of b	$2 \ln (a) + 3 \ln (b)$
23989	Simplify/Condense	2 natural log of x-0.5 natural log of x+5	$2 \ln (x) - 0.5 \ln (x + 5)$
23990	Simplify/Condense	2 natural log of x+4 natural log of y-3 natural log of z	$2 \ln (x) + 4 \ln (y) - 3 \ln (z)$
23991	Simplify/Condense	2 natural log of x+5 natural log of y- natural log of z	$2 \ln (x) + 5 \ln (y) - \ln (z)$
23992	Simplify/Condense	2 natural log of x+ natural log of x-5-3 natural log of y	$2 \ln (x) + \ln (x - 5) - 3 \ln (y)$
23993	Simplify/Condense	2 natural log of x-2 natural log of x+1-2 natural log of x-1	$2 \ln (x) - 2 \ln (x + 1) - 2 \ln (x - 1)$
23994	Simplify/Condense	21 log base m of x+4( log base m of y-3 log base m of z)	$21 \log_{m} (x + 4) (\log_{m} (y) - 3 \log_{m} (z))$
23995	Simplify/Condense	2 natural log of 3+4 natural log of 5	$2 \ln (3) + 4 \ln (5)$
23996	Simplify/Condense	2 natural log of 7x+4 natural log of x^2	$2 \ln (7 x) + 4 \ln (x^{2})$
23997	Simplify/Condense	2 natural log of 8+5 natural log of x-4	$2 \ln (8) + 5 \ln (x - 4)$
23998	Simplify/Condense	2 log of 2*(x+4)	$2 \log (2) \cdot (x + 4)$
23999	Simplify/Condense	2 log of 3+ log of 5- log of 9	$2 \log (3) + \log (5) - \log (9)$
24000	Simplify/Condense	2 log of 34+3 log of 32	$2 \log (3) \cdot 4 + 3 \log (3) \cdot 2$