Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
40101	Simplify/Condense	( natural log of 20000/16000)/5.25	$\frac{\ln (\frac{20000}{16000})}{5.25}$
40102	Simplify/Condense	( natural log of 6000/14760)/( natural log of 0.81)	$\frac{\ln (\frac{6000}{14760})}{\ln (0.81)}$
40103	Simplify/Condense	natural log of (1)^2x+3 natural log of x-10	$\ln ({(1)}^{2} x) + 3 \ln (x) - 10$
40104	Simplify/Condense	( natural log of 2)/( natural log of 9/4+ natural log of 2)	$\frac{\ln (2)}{\ln (\frac{9}{4}) + \ln (2)}$
40105	Simplify/Condense	( natural log of 22+ natural log of 11)/( log of 22+ log of 11)	$\frac{\ln (22 + \ln (11))}{\log (22 + \log (11))}$
40106	Simplify/Condense	( natural log of 253)/6	$\frac{\ln (253)}{6}$
40107	Simplify/Condense	( natural log of 3)/( natural log of 1.15)	$\frac{\ln (3)}{\ln (1.15)}$
40108	Simplify/Condense	( natural log of 3)/( natural log of 5)-7	$\frac{\ln (3)}{\ln (5)} - 7$
40109	Simplify/Condense	( natural log of 3x^2)/( natural log of e)	$\frac{\ln (3 x^{2})}{\ln (e)}$
40110	Simplify/Condense	natural log of (7)^(x^2)	$\ln ({(7)}^{x^{2}})$
40111	Simplify/Condense	( natural log of 9)/( natural log of 7/4+ natural log of 9)	$\frac{\ln (9)}{\ln (\frac{7}{4}) + \ln (9)}$
40112	Simplify/Condense	natural log of (xyz)^2	$\ln ({(x y z)}^{2})$
40113	Simplify/Condense	log of (1/5)^25	$\log ({(\frac{1}{5})}^{25})$
40114	Simplify/Condense	( log of 1/8)/( log of 64)	$\frac{\log (\frac{1}{8})}{\log (64)}$
40115	Simplify/Condense	log of (6/11)^5	$\log ({(\frac{6}{11})}^{5})$
40116	Simplify/Condense	log of (6/5)^6	$\log ({(\frac{6}{5})}^{6})$
40117	Simplify/Condense	( log of x^2+ log of x^4)/( log of 60x)	$\frac{\log (x^{2}) + \log (x^{4})}{\log (60 x)}$
40118	Simplify/Condense	log of (10)^-4	$\log ({(10)}^{- 4})$
40119	Simplify/Condense	log of (2)^6- log of (2)^15+ log of (2)^20	$\log ({(2)}^{6}) - \log ({(2)}^{15}) + \log ({(2)}^{20})$
40120	Graph	natural log of infinity	$\ln (\infty)$
40121	Simplify/Condense	( log of 3)/( log of 1.80)	$\frac{\log (3)}{\log (1.8)}$
40122	Simplify/Condense	( log of 4)/( log of 5- log of 4)	$\frac{\log (4)}{\log (5) - \log (4)}$
40123	Simplify/Condense	-( log of 90)/( log of 9)	$- \frac{\log (90)}{\log (9)}$
40124	Graph	r=6/(2-2cos(theta))	$r = \frac{6}{2 - 2 \cos (θ)}$
40125	Simplify/Condense	log base 12 of 1/12	$\log_{12} (\frac{1}{12})$
40126	Simplify/Condense	log base 13 of square root of 13	$\log_{13} (\sqrt{13})$
40127	Simplify/Condense	log base 13 of 77	$\log_{13} (77)$
40128	Simplify/Condense	log base 15 of 12	$\log_{15} (12)$
40129	Graph	2x+3y=12	$2 x + 3 y = 12$
40130	Graph	y=5sin(x/2)	$y = 5 \sin (\frac{x}{2})$
40131	Simplify/Condense	log base 2 of 37/5	$\log_{2} (\frac{37}{5})$
40132	Graph	3x-5y=15	$3 x - 5 y = 15$
40133	Graph	(x-5)^2=16(y+1)	${(x - 5)}^{2} = 16 (y + 1)$
40134	Simplify/Condense	log base 2 of x^(1/3)+ log base 2 of x^(1/2)- log base 2 of y	$\log_{2} (x^{\frac{1}{3}}) + \log_{2} (x^{\frac{1}{2}}) - \log_{2} (y)$
40135	Simplify/Condense	1/5* log base 3 of 32-2 log base 3 of x+1/2* log base 3 of y	$\frac{1}{5} \cdot \log_{3} (32) - 2 \log_{3} (x) + \frac{1}{2} \cdot \log_{3} (y)$
40136	Simplify/Condense	1/6* natural log of 8-1/6* natural log of 4	$\frac{1}{6} \cdot \ln (8) - \frac{1}{6} \cdot \ln (4)$
40137	Simplify/Condense	1/7*(3 natural log of x+2- natural log of x- natural log of x^2-64)	$\frac{1}{7} \cdot (3 \ln (x + 2) - \ln (x) - \ln (x^{2} - 64))$
40138	Simplify/Condense	10^( log of 6AB)	$10^{\log (6 A B)}$
40139	Find the Domain and Range	f(x)=3-x^2	$f (x) = 3 - x^{2}$
40140	Simplify/Condense	-2/3* log base 3 of 2m^2+1/2* log base 3 of 4m^2	$- \frac{2}{3} \cdot \log_{3} (2 m^{2}) + \frac{1}{2} \cdot \log_{3} (4 m^{2})$
40141	Simplify/Condense	2/3* log of (5.96*10^16)/(10^4.40)	$\frac{2}{3} \cdot \log (\frac{5.96 \cdot 10^{16}}{10^{4.4}})$
40142	Simplify/Condense	3/2* log base 2 of x-y-2 log base 2 of 3x+7	$\frac{3}{2} \cdot \log_{2} (x - y) - 2 \log_{2} (3 x + 7)$
40143	Simplify/Condense	343^( log base 7 of 3)	$343^{\log_{7} (3)}$
40144	Simplify/Condense	(3 natural log of 16-12)/(3-4 natural log of 16)	$\frac{3 \ln (16) - 12}{3 - 4 \ln (16)}$
40145	Simplify/Condense	-5/6* log base 2 of 2m^2+1/2* log base 2 of 4m^2	$- \frac{5}{6} \cdot \log_{2} (2 m^{2}) + \frac{1}{2} \cdot \log_{2} (4 m^{2})$
40146	Simplify/Condense	log base 1 of k+ log base 1 of p	$\log_{1} (k) + \log_{1} (p)$
40147	Simplify/Condense	log of 23/6	$\log (\frac{23}{6})$
40148	Simplify/Condense	log of x^2-36-8 log of x+6+6 log of x	$\log (x^{2} - 36) - 8 \log (x + 6) + 6 \log (x)$
40149	Simplify/Condense	log of x-3- log of x+7	$\log (x - 3) - \log (x + 7)$
40150	Find the Vertices	5x^2+8y^2=40	$5 x^{2} + 8 y^{2} = 40$
40151	Simplify/Condense	log of y+ log of 14x	$\log (y) + \log (14 x)$
40152	Simplify/Condense	log of y+ log of 3-1/3* log of x+2 log of z	$\log (y) + \log (3) - \frac{1}{3} \cdot \log (x) + 2 \log (z)$
40153	Simplify/Condense	log base 3 of 12+ log base 3 of 11+5 log base 3 of 7	$\log_{3} (12) + \log_{3} (11) + 5 \log_{3} (7)$
40154	Find the Inverse	y=(2x)/(x-3)	$y = \frac{2 x}{x - 3}$
40155	Simplify/Condense	log base 3 of 135	$\log_{3} (135)$
40156	Simplify/Condense	log base 3 of 16- log base 3 of 8	$\log_{3} (16) - \log_{3} (8)$
40157	Simplify/Condense	log base 3 of 25- log base 3 of 5	$\log_{3} (25) - \log_{3} (5)$
40158	Simplify/Condense	log base 24 of 386	$\log_{24} (386)$
40159	Simplify/Condense	log base 25 of 1/125	$\log_{25} (\frac{1}{125})$
40160	Simplify/Condense	log of 4x+7- log of x	$\log (4 x + 7) - \log (x)$
40161	Subtract	2/(2/3)-(2/3)/2	$\frac{2}{\frac{2}{3}} - \frac{\frac{2}{3}}{2}$
40162	Simplify	cos(pi/6)+sin((5pi)/6)	$\cos (\frac{π}{6}) + \sin (\frac{5 π}{6})$
40163	Simplify/Condense	log base 3 of 80	$\log_{3} (80)$
40164	Simplify	csc(theta)tan(theta)	$\csc (θ) \tan (θ)$
40165	Solve for x	(3x+2)(x-4)>0	$(3 x + 2) (x - 4) > 0$
40166	Simplify/Condense	log base 4 of 64/( square root of x+1)	$\log_{4} (\frac{64}{\sqrt{x + 1}})$
40167	Find the Range	y=2sin(x)	$y = 2 \sin (x)$
40168	Find the Domain	f(x) = square root of 4-2x	$f (x) = \sqrt{4 - 2 x}$
40169	Simplify/Condense	log base 32 of 4^(5/7)	$\log_{32} (4^{\frac{5}{7}})$
40170	Simplify/Condense	log base 32 of 4^1.5+10^(2 log of 2)	$\log_{32} (4^{1.5}) + 10^{2 \log (2)}$
40171	Simplify/Condense	log base 35 of 1/6	$\log_{35} (\frac{1}{6})$
40172	Find the Roots (Zeros)	x^3-3x^2-25x-21	$x^{3} - 3 x^{2} - 25 x - 21$
40173	Find the Roots (Zeros)	x^3-13x^2+47x-35	$x^{3} - 13 x^{2} + 47 x - 35$
40174	Solve for x	2+2x-x^2=0	$2 + 2 x - x^{2} = 0$
40175	Simplify/Condense	log base 4 of 15 square root of m/n	$\log_{4} (15 \sqrt{\frac{m}{n}})$
40176	Simplify	square root of 0.08^12	$\sqrt{{0.08}^{12}}$
40177	Simplify/Condense	log base 4 of 38/7	$\log_{4} (\frac{38}{7})$
40178	Simplify/Condense	log base 4 of 25	$\log_{4} (25)$
40179	Simplify/Condense	log base 14 of x^2-1- log base 14 of x+1	$\log_{14} (x^{2} - 1) - \log_{14} (x + 1)$
40180	Simplify	(2 square root of 5-3)/( square root of 5+1)	$\frac{2 \sqrt{5} - 3}{\sqrt{5} + 1}$
40181	Solve for x	(e^x+100e^(-x))/2=10	$\frac{e^{x} + 100 e^{- x}}{2} = 10$
40182	Simplify/Condense	log base 4 of 44	$\log_{4} (44)$
40183	Simplify/Condense	log base 2 of 6- log base 2 of 15+ log base 2 of 80	$\log_{2} (6) - \log_{2} (15) + \log_{2} (80)$
40184	Simplify/Condense	log base 2 of 625- log base 2 of 125+3 log base 2 of 3	$\log_{2} (625) - \log_{2} (125) + 3 \log_{2} (3)$
40185	Simplify/Condense	log base 2 of 68	$\log_{2} (68)$
40186	Simplify/Condense	log base 2 of 8x	$\log_{2} (8 x)$
40187	Simplify/Condense	log base 2 of 9* log base 3 of 25* log base 5 of 4	$\log_{2} (9) \cdot \log_{3} (25) \cdot \log_{5} (4)$
40188	Solve for x	9^(4x+2)=27	$9^{4 x + 2} = 27$
40189	Simplify/Condense	log base 2 of xyz	$\log_{2} (x y z)$
40190	Simplify/Condense	log base 200 of 50	$\log_{200} (50)$
40191	Simplify/Condense	log base 3 of 405/x	$\log_{3} (\frac{405}{x})$
40192	Solve for x	8cos(x)+4=0	$8 \cos (x) + 4 = 0$
40193	Simplify/Condense	log base 3 of seventh root of 3	$\log_{3} (\sqrt[7]{3})$
40194	Simplify/Condense	log base 3 of x^6+ log base 3 of 18x^3- log base 3 of 18	$\log_{3} (x^{6}) + \log_{3} (18 x^{3}) - \log_{3} (18)$
40195	Simplify/Condense	log base 3 of 0.015	$\log_{3} (0.015)$
40196	Simplify/Condense	log base 100 of 0.3	$\log_{100} (0.3)$
40197	Simplify/Condense	log base 1000 of 45	$\log_{1000} (45)$
40198	Simplify/Condense	log base 2 of 10x	$\log_{2} (10 x)$
40199	Simplify/Condense	log base 2 of 3* log base 3 of 4* log base 4 of 5* log base 5 of 6* log base 7 of 8	$\log_{2} (3) \cdot \log_{3} (4) \cdot \log_{4} (5) \cdot \log_{5} (6) \cdot \log_{7} (8)$
40200	Simplify/Condense	log base 2 of 3 square root of 2	$\log_{2} (3 \sqrt{2})$