Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
17401	Find the Center and Radius	x^2+y^2-4x-12y+31=0	$x^{2} + y^{2} - 4 x - 12 y + 31 = 0$
17402	Find the Center and Radius	x^2+y^2-4x-12y-9=0	$x^{2} + y^{2} - 4 x - 12 y - 9 = 0$
17403	Find the Center and Radius	x^2+y^2-4x+2y-44=0	$x^{2} + y^{2} - 4 x + 2 y - 44 = 0$
17404	Find the Center and Radius	x^2+y^2-2x-8y-19=0	$x^{2} + y^{2} - 2 x - 8 y - 19 = 0$
17405	Find the Center and Radius	x^2+y^2-6x+2y-6=0	$x^{2} + y^{2} - 6 x + 2 y - 6 = 0$
17406	Find the Center and Radius	x^2+y^2-4x-2y-31=0	$x^{2} + y^{2} - 4 x - 2 y - 31 = 0$
17407	Find the Center and Radius	x^2+y^2-4x-6y=33	$x^{2} + y^{2} - 4 x - 6 y = 33$
17408	Find the Center and Radius	x^2+y^2-4x-6y-12=0	$x^{2} + y^{2} - 4 x - 6 y - 12 = 0$
17409	Find the Center and Radius	x^2+y^2-7x=15-2y	$x^{2} + y^{2} - 7 x = 15 - 2 y$
17410	Find the Center and Radius	x^2+y^2-6x=0	$x^{2} + y^{2} - 6 x = 0$
17411	Find the Center and Radius	x^2+y^2-6x-8y+16=0	$x^{2} + y^{2} - 6 x - 8 y + 16 = 0$
17412	Find the Center and Radius	x^2+y^2-6x-4y-12=0	$x^{2} + y^{2} - 6 x - 4 y - 12 = 0$
17413	Find the Center and Radius	x^2+y^2-6x-8y=0	$x^{2} + y^{2} - 6 x - 8 y = 0$
17414	Find the Center and Radius	x^2+y^2-8x-10y+40=0	$x^{2} + y^{2} - 8 x - 10 y + 40 = 0$
17415	Find the Center and Radius	x^2+y^2-8x-10y-8=0	$x^{2} + y^{2} - 8 x - 10 y - 8 = 0$
17416	Find the Center and Radius	x^2+10x+y^2-8y=-40	$x^{2} + 10 x + y^{2} - 8 y = - 40$
17417	Find the Center and Radius	x^2+y^2+8x-6y-15=0	$x^{2} + y^{2} + 8 x - 6 y - 15 = 0$
17418	Find the Center and Radius	x^2+y^2+9x-4y-2=0	$x^{2} + y^{2} + 9 x - 4 y - 2 = 0$
17419	Find the Center and Radius	x^2+y^2-10x+2y+22=0	$x^{2} + y^{2} - 10 x + 2 y + 22 = 0$
17420	Find the Center and Radius	x^2+y^2-2x-6y+1=0	$x^{2} + y^{2} - 2 x - 6 y + 1 = 0$
17421	Find the Center and Radius	x^2+y^2-2x-4y-31=0	$x^{2} + y^{2} - 2 x - 4 y - 31 = 0$
17422	Find the Center and Radius	x^2+y^2-18x-20y+144=0	$x^{2} + y^{2} - 18 x - 20 y + 144 = 0$
17423	Find the Center and Radius	x^2+y^2-12x+18y+36=0	$x^{2} + y^{2} - 12 x + 18 y + 36 = 0$
17424	Find the Center and Radius	x^2+y^2-12x+2y+12=0	$x^{2} + y^{2} - 12 x + 2 y + 12 = 0$
17425	Find the Center and Radius	x^2+y^2-12y=0	$x^{2} + y^{2} - 12 y = 0$
17426	Simplify/Condense	3 log of x+1/2* log of y-2 log of z-2/3* log of 8	$3 \log (x) + \frac{1}{2} \cdot \log (y) - 2 \log (z) - \frac{2}{3} \cdot \log (8)$
17427	Simplify/Condense	3 log of x-2+2 log of x+2	$3 \log (x - 2) + 2 \log (x + 2)$
17428	Simplify/Condense	4 log base 6 of 12-24 log base 6 of 7	$4 \log_{6} (12) - 24 \log_{6} (7)$
17429	Simplify/Condense	4 log base 8 of x-7-5 log base 8 of x+5	$4 \log_{8} (x - 7) - 5 \log_{8} (x + 5)$
17430	Simplify/Condense	4 log of x-2 log of x-3	$4 \log (x) - 2 \log (x - 3)$
17431	Simplify/Condense	5 natural log of x-1/2* natural log of y+6 natural log of z	$5 \ln (x) - \frac{1}{2} \cdot \ln (y) + 6 \ln (z)$
17432	Simplify/Condense	2 log of x+5 log of y	$2 \log (x) + 5 \log (y)$
17433	Simplify/Condense	2.7 natural log of 7x^2	$2.7 \ln (7 x^{2})$
17434	Simplify/Condense	3 log base 6 of x+5 log base 6 of x-6	$3 \log_{6} (x + 5 \log_{6} (x - 6))$
17435	Simplify/Condense	1-2 log base 7 of x	$1 - 2 \log_{7} (x)$
17436	Simplify/Condense	2 log base 3 of u- log base 3 of v	$2 \log_{3} (u) - \log_{3} (v)$
17437	Simplify/Condense	log base 2 of 16x+40y	$\log_{2} (16 x + 40 y)$
17438	Simplify/Condense	log base 2 of 12-2 log base 2 of 6+ log base 2 of 24	$\log_{2} (12) - 2 \log_{2} (6) + \log_{2} (24)$
17439	Simplify/Condense	log base 2 of 5-1/2* log base 2 of 169	$\log_{2} (5) - \frac{1}{2} \cdot \log_{2} (169)$
17440	Simplify/Condense	log base 2 of 6* log base 6 of 4	$\log_{2} (6) \cdot \log_{6} (4)$
17441	Find the Asymptotes	tan(x)	$\tan (x)$
17442	Simplify/Condense	log base 2 of 1/( fifth root of 16)	$\log_{2} (\frac{1}{\sqrt[5]{16}})$
17443	Simplify/Condense	log base 2 of 5^2*4^5	$\log_{2} (5^{2} \cdot 4^{5})$
17444	Simplify/Condense	( log of 625)/( log of 125)	$\frac{\log (625)}{\log (125)}$
17445	Simplify/Condense	3/2* log base 2 of x-y-2 log base 2 of x^2+y^2	$\frac{3}{2} \cdot \log_{2} (x - y) - 2 \log_{2} (x^{2} + y^{2})$
17446	Simplify/Condense	-3/4* log base 3 of 16p^4-2/3* log base 3 of 8p^3	$- \frac{3}{4} \cdot \log_{3} (16 p^{4}) - \frac{2}{3} \cdot \log_{3} (8 p^{3})$
17447	Simplify/Condense	log base 11 of 121	$\log_{11} (121)$
17448	Simplify/Condense	log base 3 of (x^2-x-2)/(x^2+3x-4)	$\log_{3} (\frac{x^{2} - x - 2}{x^{2} + 3 x - 4})$
17449	Simplify/Condense	log base 4 of x^2-64-4 log base 4 of x+8	$\log_{4} (x^{2} - 64) - 4 \log_{4} (x + 8)$
17450	Simplify/Condense	log base 6 of 1/36- log base 2 of 16	$\log_{6} (\frac{1}{36}) - \log_{2} (16)$
17451	Simplify/Condense	log base 6 of 15	$\log_{6} (15)$
17452	Simplify/Condense	log base 7 of 1/7	$\log_{7} (\frac{1}{7})$
17453	Simplify/Condense	log base 9 of ( fourth root of 27)/3	$\log_{9} (\frac{\sqrt[4]{27}}{3})$
17454	Simplify/Condense	log base 9 of 18+ log base 9 of 36-3 log base 9 of 2	$\log_{9} (18) + \log_{9} (36) - 3 \log_{9} (2)$
17455	Simplify/Condense	log base 9 of 11z	$\log_{9} (11 z)$
17456	Simplify/Condense	log base 8 of 16- log base 8 of 2	$\log_{8} (16) - \log_{8} (2)$
17457	Simplify/Condense	log base 7 of 3- log base 7 of 8	$\log_{7} (3) - \log_{7} (8)$
17458	Simplify/Condense	log base 7 of 6* log base 6 of 343	$\log_{7} (6) \cdot \log_{6} (343)$
17459	Simplify/Condense	log base 8 of x^2-81- log base 8 of x-9	$\log_{8} (x^{2} - 81) - \log_{8} (x - 9)$
17460	Simplify/Condense	log base 7 of 0.17	$\log_{7} (0.17)$
17461	Simplify/Condense	log base 7 of 25	$\log_{7} (25)$
17462	Simplify/Condense	log base 7 of 1/8	$\log_{7} (\frac{1}{8})$
17463	Simplify/Condense	log base r of 12+ log base r of 45	$\log_{r} (12) + \log_{r} (45)$
17464	Simplify/Condense	x^( natural log of x)	$x^{\ln (x)}$
17465	Simplify/Condense	10 log of cube root of x	$10 \log (\sqrt[3]{x})$
17466	Simplify/Condense	0.5+ log of 9+( natural log of 15- natural log of 3)/( natural log of 75- natural log of 3)-( natural log of 9)/( natural log of 10)	$0.5 + \log (9) + \frac{\ln (15) - \ln (3)}{\ln (75) - \ln (3)} - \frac{\ln (9)}{\ln (10)}$
17467	Simplify/Condense	log base a of x^2-9- log base a of x-3	$\log_{a} (x^{2} - 9) - \log_{a} (x - 3)$
17468	Simplify/Condense	log base b of cube root of 3	$\log_{b} (\sqrt[3]{3})$
17469	Simplify/Condense	log base 9 of 7+ log base 9 of 5/7	$\log_{9} (7) + \log_{9} (\frac{5}{7})$
17470	Simplify/Condense	log base 5 of 9	$\log_{5} (9)$
17471	Simplify/Condense	log base 5 of 700	$\log_{5} (700)$
17472	Simplify/Condense	log base 6 of 36x	$\log_{6} (36 x)$
17473	Simplify/Condense	log base 6 of square root of x- log base 6 of x^6	$\log_{6} (\sqrt{x}) - \log_{6} (x^{6})$
17474	Simplify/Condense	log base 6 of 11* log base 11 of 16* log base 16 of 21* log base 21 of 26* log base 26 of 31* log base 31 of 36	$\log_{6} (11) \cdot \log_{11} (16) \cdot \log_{16} (21) \cdot \log_{21} (26) \cdot \log_{26} (31) \cdot \log_{31} (36)$
17475	Simplify/Condense	log base 5 of sin(pi/8)- log base 5 of cos(pi/8)	$\log_{5} (\sin (\frac{π}{8})) - \log_{5} (\cos (\frac{π}{8}))$
17476	Simplify/Condense	log base 6 of cube root of 6	$\log_{6} (\sqrt[3]{6})$
17477	Simplify/Condense	log base 5 of 50	$\log_{5} (50)$
17478	Simplify/Condense	log base 5 of 10+ log base 5 of 20-3 log base 5 of 2	$\log_{5} (10) + \log_{5} (20) - 3 \log_{5} (2)$
17479	Simplify/Condense	log base 3 of 32- log base 3 of 128+3 log base 3 of 4	$\log_{3} (32) - \log_{3} (128) + 3 \log_{3} (4)$
17480	Simplify/Condense	log base 4 of 20- log base 4 of 45+ log base 4 of 144	$\log_{4} (20) - \log_{4} (45) + \log_{4} (144)$
17481	Simplify/Condense	log base 4 of x^2+14x+45- log base 4 of x+5	$\log_{4} (x^{2} + 14 x + 45) - \log_{4} (x + 5)$
17482	Simplify/Condense	log base 4 of 128+ log base 8 of 256	$\log_{4} (128) + \log_{8} (256)$
17483	Simplify/Condense	2 log of x+3 log of y-5 log of x	$2 \log (x) + 3 \log (y) - 5 \log (x)$
17484	Simplify/Condense	3 log base 6 of x+5 log base 6 of x-6	$3 \log_{6} (x + 5) \log_{6} (x - 6)$
17485	Simplify/Condense	3 log base 2 of x+2 log base 2 of y-3 log base 2 of z	$3 \log_{2} (x) + 2 \log_{2} (y) - 3 \log_{2} (z)$
17486	Simplify/Condense	2 log of -2y^-1	$2 \log (- 2 y^{- 1})$
17487	Simplify/Condense	2 log of x^5y^2+7 log of 1/x-3 log of y	$2 \log (x^{5} y^{2}) + 7 \log (\frac{1}{x}) - 3 \log (y)$
17488	Simplify/Condense	2 log of 7	$2 \log (7)$
17489	Simplify/Condense	2 natural log of square root of e+e^( natural log of 3)	$2 \ln (\sqrt{e}) + e^{\ln (3)}$
17490	Simplify/Condense	2 natural log of 3x+ natural log of 5x- natural log of 6xy	$2 \ln (3 x) + \ln (5 x) - \ln (6 x y)$
17491	Simplify/Condense	2 natural log of x-1/2* natural log of y	$2 \ln (x) - \frac{1}{2} \cdot \ln (y)$
17492	Simplify/Condense	3 log base 5 of x-1/2* log base 5 of 6-x	$3 \log_{5} (x) - \frac{1}{2} \cdot \log_{5} (6 - x)$
17493	Simplify/Condense	3- natural log of e^(x^2+2)	$3 - \ln (e^{x^{2} + 2})$
17494	Simplify/Condense	3 log base 2 of u+2 log base 2 of v	$3 \log_{2} (u) + 2 \log_{2} (v)$
17495	Simplify/Condense	3 log base 5 of 3x+1-2 log base 5 of 2x-1- log base 5 of x	$3 \log_{5} (3 x + 1) - 2 \log_{5} (2 x - 1) - \log_{5} (x)$
17496	Simplify/Condense	3 log base 4 of x+1/6* log base 4 of y	$3 \log_{4} (x) + \frac{1}{6} \cdot \log_{4} (y)$
17497	Simplify/Condense	3 log base 3 of 5- log base 3 of 4	$3 \log_{3} (5) - \log_{3} (4)$
17498	Simplify/Condense	3 log base 4 of x^2+1/2* log base 4 of square root of x	$3 \log_{4} (x^{2}) + \frac{1}{2} \cdot \log_{4} (\sqrt{x})$
17499	Solve for x	3x^2+13x+10=0	$3 x^{2} + 13 x + 10 = 0$
17500	Simplify/Condense	2 log base 2 of x-9+ log base 2 of 2=3	$2 \log_{2} (x - 9) + \log_{2} (2) = 3$