Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
24701	Find the Center and Radius	2x^2+14x+2y^2+6y=-2	$2 x^{2} + 14 x + 2 y^{2} + 6 y = - 2$
24702	Find the Center and Radius	x^2-4x+y^2+12y+4=0	$x^{2} - 4 x + y^{2} + 12 y + 4 = 0$
24703	Find the Center and Radius	10x^2-80x+10y^2-40y=30	$10 x^{2} - 80 x + 10 y^{2} - 40 y = 30$
24704	Find the Center and Radius	13x^2-49=-13y^2	$13 x^{2} - 49 = - 13 y^{2}$
24705	Find the Center and Radius	144x^2+144y^2-96x+72y-11=0	$144 x^{2} + 144 y^{2} - 96 x + 72 y - 11 = 0$
24706	Find the Center and Radius	16x^2+16y^2-48x+8y=27	$16 x^{2} + 16 y^{2} - 48 x + 8 y = 27$
24707	Find the Center and Radius	16x^2-64x+16y^2+48y-69=0	$16 x^{2} - 64 x + 16 y^{2} + 48 y - 69 = 0$
24708	Find the Center and Radius	18x^2+18y^2-12x+9y-7=0	$18 x^{2} + 18 y^{2} - 12 x + 9 y - 7 = 0$
24709	Find the Center and Radius	2(x+2)^2+2(y+3)^2=72	$2 {(x + 2)}^{2} + 2 {(y + 3)}^{2} = 72$
24710	Find the Center and Radius	2x^2+18x+2y^2-4y=-69/2	$2 x^{2} + 18 x + 2 y^{2} - 4 y = - \frac{69}{2}$
24711	Find the Center and Radius	2x^2+2y^2+12x+8y+8=0	$2 x^{2} + 2 y^{2} + 12 x + 8 y + 8 = 0$
24712	Find the Center and Radius	2x^2+2y^2+12x-20y+36=0	$2 x^{2} + 2 y^{2} + 12 x - 20 y + 36 = 0$
24713	Find the Center and Radius	2x^2+2y^2+12x-4y+12=0	$2 x^{2} + 2 y^{2} + 12 x - 4 y + 12 = 0$
24714	Find the Center and Radius	2x^2+2y^2+12y=0	$2 x^{2} + 2 y^{2} + 12 y = 0$
24715	Find the Center and Radius	2x^2+2y^2+4y=0	$2 x^{2} + 2 y^{2} + 4 y = 0$
24716	Find the Center and Radius	2x^2+2y^2+4y-23=0	$2 x^{2} + 2 y^{2} + 4 y - 23 = 0$
24717	Find the Center and Radius	2x^2+2y^2+50x+20y=-24	$2 x^{2} + 2 y^{2} + 50 x + 20 y = - 24$
24718	Find the Center and Radius	2x^2+2y^2=50	$2 x^{2} + 2 y^{2} = 50$
24719	Find the Center and Radius	2x^2+2y^2=8	$2 x^{2} + 2 y^{2} = 8$
24720	Find the Center and Radius	x^2-12x+21+y^2+2y=0	$x^{2} - 12 x + 21 + y^{2} + 2 y = 0$
24721	Find the Center and Radius	2x^2+2y^2+8x-42=0	$2 x^{2} + 2 y^{2} + 8 x - 42 = 0$
24722	Find the Center and Radius	2x^2+2y^2+8x-4y+9=0	$2 x^{2} + 2 y^{2} + 8 x - 4 y + 9 = 0$
24723	Find the Center and Radius	2x^2+2y^2=1	$2 x^{2} + 2 y^{2} = 1$
24724	Simplify/Condense	(1/2) log of x+(1/3) log of y-2 log of z	$(\frac{1}{2}) \log (x) + (\frac{1}{3}) \log (y) - 2 \log (z)$
24725	Simplify/Condense	(1/3) log base 4 of 2a+(1/3) log base 4 of 5b-2 log base 4 of a- log base 4 of b	$(\frac{1}{3}) \log_{4} (2 a) + (\frac{1}{3}) \log_{4} (5 b) - 2 \log_{4} (a) - \log_{4} (b)$
24726	Simplify/Condense	(( natural log of 0.60)/2)*6	$(\frac{\ln (0.6)}{2}) \cdot 6$
24727	Simplify/Condense	( log of 12- log of 1/12)/( log of 7)	$\frac{\log (12) - \log (\frac{1}{12})}{\log (7)}$
24728	Simplify/Condense	( log base b of 93.1699)( log base b of 52.3219)( log base b of 225)	$(\log_{b} (9) \cdot 3.1699) (\log_{b} (5) \cdot 2.3219) (\log_{b} (225))$
24729	Simplify/Condense	(2x-1) log base 4 of 16	$(2 x - 1) \log_{4} (16)$
24730	Simplify/Condense	(30(-5)+8000) natural log of 76/p	$(30 (- 5) + 8000) \ln (\frac{76}{p})$
24731	Simplify/Condense	(3-x) log of 8	$(3 - x) \log (8)$
24732	Simplify/Condense	(-6+ log base 4 of x)-3(-6 log base 4 of x)-8	$(- 6 + \log_{4} (x)) - 3 (- 6 \log_{4} (x)) - 8$
24733	Simplify/Condense	( log of a+ log of b)- log of c	$(\log (a) + \log (b)) - \log (c)$
24734	Simplify/Condense	(x+4) log of 12	$(x + 4) \log (12)$
24735	Simplify/Condense	0.25 log of x- log of y- log of z^2	$0.25 \log (x) - \log (y) - \log (z^{2})$
24736	Simplify/Condense	0.3(2 log of x+5- log of x- log of x^2-4)	$0.3 (2 \log (x + 5) - \log (x) - \log (x^{2} - 4))$
24737	Simplify/Condense	0.66 natural log of e^12	$0.66 \ln (e^{12})$
24738	Simplify/Condense	(2 log base 5 of x+ log base 5 of x-1)-4 log base 5 of w	$(2 \log_{5} (x) + \log_{5} (x - 1)) - 4 \log_{5} (w)$
24739	Find the Center and Radius	8x^2-72x+8y^2-24y-332=0	$8 x^{2} - 72 x + 8 y^{2} - 24 y - 332 = 0$
24740	Find the Center and Radius	8x+x^2-2y=64-y^2	$8 x + x^{2} - 2 y = 64 - y^{2}$
24741	Find the Center and Radius	9x^2+54x+9y^2-6y+19=0	$9 x^{2} + 54 x + 9 y^{2} - 6 y + 19 = 0$
24742	Find the Center and Radius	6x^2+6y^2+24x+36y-18=0	$6 x^{2} + 6 y^{2} + 24 x + 36 y - 18 = 0$
24743	Simplify/Condense	6 log of 25-x^2	$6 \log (25 - x^{2})$
24744	Simplify/Condense	( log of 40+3 log of 2)- log of 32	$(\log (40) + 3 \log (2)) - \log (32)$
24745	Find the Center and Radius	9x^2+9y^2+126x-54y+353=0	$9 x^{2} + 9 y^{2} + 126 x - 54 y + 353 = 0$
24746	Simplify/Condense	( log of 3)/( log of 0.4)	$\frac{\log (3)}{\log (0.4)}$
24747	Simplify/Condense	log base 2 of (32)^5	$\log_{2} ({(32)}^{5})$
24748	Simplify/Condense	log base 22 of (22)^4	$\log_{22} ({(22)}^{4})$
24749	Simplify/Condense	log base 5 of (5)^71	$\log_{5} ({(5)}^{71})$
24750	Simplify/Condense	( log of 11 log of 3 log of 11)/(2 log of 16)	$\frac{\log (11) \log (3) \log (11)}{2 \log (16)}$
24751	Simplify/Condense	( log of (1)^(x-3))/( log of (1)^4)	$\frac{\log ({(1)}^{x - 3})}{\log ({(1)}^{4})}$
24752	Simplify/Condense	( log base 1 of 36)/6	$\frac{\log_{1} (36)}{6}$
24753	Simplify/Condense	( log base 7 of cube root of x square root of y)/(z^2)	$\frac{\log_{7} (\sqrt[3]{x} \sqrt{y})}{z^{2}}$
24754	Simplify/Condense	log base 8 of ((y^4 square root of x)/(3z^2))^3	$\log_{8} ({(\frac{y^{4} \sqrt{x}}{3 z^{2}})}^{3})$
24755	Simplify/Condense	1/2*( natural log of 4+3)	$\frac{1}{2} \cdot (\ln (4 + 3))$
24756	Simplify/Condense	1/2*(4 natural log of x- natural log of y- natural log of z)	$\frac{1}{2} \cdot (4 \ln (x) - \ln (y) - \ln (z))$
24757	Simplify/Condense	1/2* log base 2 of (x)^4+1/4* log base 2 of (x)^4-1/6* log base 2 of x	$\frac{1}{2} \cdot \log_{2} ({(x)}^{4}) + \frac{1}{4} \cdot \log_{2} ({(x)}^{4}) - \frac{1}{6} \cdot \log_{2} (x)$
24758	Simplify/Condense	1/2* log base 2 of 1/64	$\frac{1}{2} \cdot \log_{2} (\frac{1}{64})$
24759	Simplify/Condense	1/2* log base 2 of x+4 log base 2 of w- log base 2 of y	$\frac{1}{2} \cdot \log_{2} (x) + 4 \log_{2} (w) - \log_{2} (y)$
24760	Simplify/Condense	1/2* log base 2 of x-8 log base 2 of y-5 log base 2 of z	$\frac{1}{2} \cdot \log_{2} (x) - 8 \log_{2} (y - 5) \log_{2} (z)$
24761	Simplify/Condense	1/2* log base 5 of x+2 log base 5 of y-3 log base 5 of z	$\frac{1}{2} \cdot \log_{5} (x) + 2 \log_{5} (y) - 3 \log_{5} (z)$
24762	Simplify/Condense	0.2/(1.00+0.90)7.2 log of 115.20/86.4	$\frac{0.2}{1 + 0.9} \cdot 7.2 \cdot \log (\frac{115.2}{86.4})$
24763	Simplify/Condense	1/0.3321* natural log of 35000/10500	$\frac{1}{0.3321} \cdot \ln (\frac{35000}{10500})$
24764	Simplify/Condense	1/0.000013* natural log of 1.225/(1100(0.000013)sin(12))	$\frac{1}{0.000013} \cdot \ln (\frac{1.225}{1100 (0.000013) \sin (12)})$
24765	Simplify/Condense	1/18* log of 7.34+10 log of 2468	$\frac{1}{18} \cdot \log (7.34) + 10 \log (2468)$
24766	Simplify/Condense	1/2(1/3 log of x-3+6 log of x-1)-10 log of x	$\frac{1}{2} \cdot (\frac{1}{3} \cdot \log (x - 3) + 6 \log (x - 1)) - 10 \log (x)$
24767	Simplify/Condense	1/2*( log base 5 of x+1+ log base 5 of y)+2 log base 5 of x+1	$\frac{1}{2} \cdot (\log_{5} (x + 1) + \log_{5} (y)) + 2 \log_{5} (x + 1)$
24768	Simplify/Condense	1/2* log base 7 of x+ log base 7 of y-4 log base 7 of x+5	$\frac{1}{2} \cdot \log_{7} (x) + \log_{7} (y) - 4 \log_{7} (x + 5)$
24769	Simplify/Condense	1/2* log base 8 of w+7 log base 8 of z- log base 8 of y	$\frac{1}{2} \cdot \log_{8} (w) + 7 \log_{8} (z) - \log_{8} (y)$
24770	Simplify/Condense	1/2* log base 9 of 9x^4-6 log base b of y	$\frac{1}{2} \cdot \log_{9} (9 x^{4}) - 6 \log_{b} (y)$
24771	Simplify/Condense	1/2* log base c of w+3 log base c of x- log base c of z	$\frac{1}{2} \cdot \log_{c} (w) + 3 \log_{c} (x) - \log_{c} (z)$
24772	Simplify/Condense	1/2* natural log of x^2+4	$\frac{1}{2} \cdot \ln (x^{2} + 4)$
24773	Simplify/Condense	1/2* natural log of 3+ natural log of 9	$\frac{1}{2} \cdot \ln (3) + \ln (9)$
24774	Simplify/Condense	1/2* log of 4/729	$\frac{1}{2} \cdot \log (\frac{4}{729})$
24775	Simplify/Condense	1/2* log of 36-1/3* log of 64	$\frac{1}{2} \cdot \log (36) - \frac{1}{3} \cdot \log (64)$
24776	Simplify/Condense	1/2* log of 64-3 log of 2+ log of 100	$\frac{1}{2} \cdot \log (64) - 3 \log (2) + \log (100)$
24777	Simplify/Condense	1/2* log of 81- log of 3	$\frac{1}{2} \cdot \log (81) - \log (3)$
24778	Simplify/Condense	1/2* log of x-3 log of y+1/3* log of m	$\frac{1}{2} \cdot \log (x) - 3 \log (y) + \frac{1}{3} \cdot \log (m)$
24779	Simplify/Condense	1/3*( log base 4 of x- log base 4 of y)+2 log base 4 of x-5	$\frac{1}{3} \cdot (\log_{4} (x - \log_{4} (y))) + 2 \log_{4} (x - 5)$
24780	Simplify/Condense	1/3*(( natural log of 11/4)/( natural log of 2)+2)	$\frac{1}{3} \cdot (\frac{\ln (\frac{11}{4})}{\ln (2)} + 2)$
24781	Simplify/Condense	(3 natural log of 3)/( natural log of 3+8 natural log of 7)	$\frac{3 \ln (3)}{\ln (3) + 8 \ln (7)}$
24782	Simplify/Condense	4^(( natural log of 3)/( natural log of 2))	$4^{\frac{\ln (3)}{\ln (2)}}$
24783	Simplify/Condense	4^( log base 16 of 7)	$4^{\log_{16} (7)}$
24784	Simplify/Condense	5/2* natural log of 4x^6-3/5* natural log of 2y^10	$\frac{5}{2} \cdot \ln (4 x^{6}) - \frac{3}{5} \cdot \ln (2 y^{10})$
24785	Simplify/Condense	5/6* log base 2 of x+2/3* log base 2 of y-1/2* log base 2 of x- log base 2 of x	$\frac{5}{6} \cdot \log_{2} (x) + \frac{2}{3} \cdot \log_{2} (y) - \frac{1}{2} \cdot \log_{2} (x) - \log_{2} (x)$
24786	Simplify/Condense	5/7*( log of 5(x/y))	$\frac{5}{7} \cdot (\log (5) (\frac{x}{y}))$
24787	Simplify/Condense	(5 log of x)/2	$\frac{5 \log (x)}{2}$
24788	Simplify/Condense	6/7* log base 2 of x-7 log base 2 of y	$\frac{6}{7} \cdot \log_{2} (x) - 7 \log_{2} (y)$
24789	Simplify/Condense	6^( log of 6*9)	$6^{\log (6) \cdot 9}$
24790	Simplify/Condense	7/2* log base 7 of z+3	$\frac{7}{2} \cdot \log_{7} (z + 3)$
24791	Simplify/Condense	8^(7 log base 8 of x)	$8^{7 \log_{8} (x)}$
24792	Simplify/Condense	8^( log of 8^k)	$8^{\log (8^{k})}$
24793	Evaluate	1/2*(cos(465)cos(75))	$\frac{1}{2} \cdot (\cos (465) \cos (75))$
24794	Simplify/Condense	e^(2-4 natural log of x+ natural log of y)	$e^{2 - 4 \ln (x) + \ln (y)}$
24795	Simplify/Condense	e^4-8 natural log of x+ natural log of y	$e^{4} - 8 \ln (x) + \ln (y)$
24796	Simplify/Condense	e^(6-2 natural log of x+ natural log of y)	$e^{6 - 2 \ln (x) + \ln (y)}$
24797	Simplify/Condense	e^(6 natural log of x)	$e^{6 \ln (x)}$
24798	Simplify/Condense	e^( natural log of x+ natural log of 3-3)	$e^{\ln (x) + \ln (3) - 3}$
24799	Simplify/Condense	( natural log of 0.27)/-0.000121	$\frac{\ln (0.27)}{- 0.000121}$
24800	Graph	(y^2)/12-(x^2)/4=1	$\frac{y^{2}}{12} - \frac{x^{2}}{4} = 1$