Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
32001	Evaluate	log base 4 of (3)^4+ log base 4 of 9	$\log_{4} ({(3)}^{4}) + \log_{4} (9)$
32002	Evaluate	log base 4 of (4)^(5/6)	$\log_{4} ({(4)}^{\frac{5}{6}})$
32003	Evaluate	log base 4 of (4)^4	$\log_{4} ({(4)}^{4})$
32004	Evaluate	log base 5 of (2)^3+ log base 5 of 4	$\log_{5} ({(2)}^{3}) + \log_{5} (4)$
32005	Evaluate	( log base 5 of 22)/( log base 5 of 4)	$\frac{\log_{5} (22)}{\log_{5} (4)}$
32006	Evaluate	( log base 5 of 25x^2(y+1)^3)/( log base 5 of (2z-1)^3 fifth root of (x-4)^3)	$\frac{\log_{5} (25 x^{2} {(y + 1)}^{3})}{\log_{5} ({(2 z - 1)}^{3} \sqrt[5]{{(x - 4)}^{3}})}$
32007	Evaluate	( log base 5 of 25x^6y^7)/(z^2)	$\frac{\log_{5} (25 x^{6} y^{7})}{z^{2}}$
32008	Evaluate	( log base 5 of 2500)/2	$\frac{\log_{5} (2500)}{2}$
32009	Evaluate	( log base 5 of 36)/( log base 5 of 6)	$\frac{\log_{5} (36)}{\log_{5} (6)}$
32010	Evaluate	( log base 5 of 49)/( log base 5 of 1/7)	$\frac{\log_{5} (49)}{\log_{5} (\frac{1}{7})}$
32011	Evaluate	log base 4 of (55)^10	$\log_{4} ({(55)}^{10})$
32012	Evaluate	( log base 4 of 64)/( log base 16 of 4)	$\frac{\log_{4} (64)}{\log_{16} (4)}$
32013	Evaluate	log base 4 of (64)^5	$\log_{4} ({(64)}^{5})$
32014	Evaluate	( log base 4 of 81- log base p of 1)/( log base 4.24 of 18- log of 0.01)	$\frac{\log_{4} (81) - \log_{p} (1)}{\log_{4.24} (18) - \log (0.01)}$
32015	Evaluate	log base 5 of ((a^4)/(b^2))^3	$\log_{5} ({(\frac{a^{4}}{b^{2}})}^{3})$
32016	Evaluate	log base 5 of (1/125)^-3	$\log_{5} ({(\frac{1}{125})}^{- 3})$
32017	Evaluate	log base 5 of (u square root of t)^3	$\log_{5} ({(u \sqrt{t})}^{3})$
32018	Evaluate	log base 5 of (xy)^6	$\log_{5} ({(x y)}^{6})$
32019	Evaluate	log base 5 of (5)^6	$\log_{5} ({(5)}^{6})$
32020	Evaluate	log base 5 of (5)^82	$\log_{5} ({(5)}^{82})$
32021	Evaluate	log base 5 of (7)^4	$\log_{5} ({(7)}^{4})$
32022	Evaluate	log base 3 of (81)^-5	$\log_{3} ({(81)}^{- 5})$
32023	Evaluate	log base 3 of (9)^100	$\log_{3} ({(9)}^{100})$
32024	Evaluate	( log base 3 of 27+8 log base 16 of 2)/( log base 8 of 512)* log base 1000 of 10	$\frac{\log_{3} (27) + 8 \log_{16} (2)}{\log_{8} (512)} \cdot \log_{1000} (10)$
32025	Evaluate	log base 5 of (125)^-1	$\log_{5} ({(125)}^{- 1})$
32026	Evaluate	log base 5 of (125)^2	$\log_{5} ({(125)}^{2})$
32027	Evaluate	( log base 2 of 27)/-3	$\frac{\log_{2} (27)}{- 3}$
32028	Evaluate	( log base 2 of 27+1)/3	$\frac{\log_{2} (27 + 1)}{3}$
32029	Evaluate	log base 2 of (32)^(2/5)	$\log_{2} ({(32)}^{\frac{2}{5}})$
32030	Evaluate	log base 2 of (4)^400	$\log_{2} ({(4)}^{400})$
32031	Evaluate	log base 2 of (4)^500	$\log_{2} ({(4)}^{500})$
32032	Evaluate	log base 2 of (4)^600	$\log_{2} ({(4)}^{600})$
32033	Evaluate	( log base 2 of 4a)/( log base 2 of 2a)	$\frac{\log_{2} (4 a)}{\log_{2} (2 a)}$
32034	Evaluate	( log base 2 of 5000)/3	$\frac{\log_{2} (5000)}{3}$
32035	Evaluate	log base 2 of (8)^(1/7)	$\log_{2} ({(8)}^{\frac{1}{7}})$
32036	Evaluate	log base 2 of (MN)^4	$\log_{2} ({(M N)}^{4})$
32037	Evaluate	log base 27 of (9)^( log of 1000)	$\log_{27} ({(9)}^{\log (1000)})$
32038	Evaluate	( log base 3 of x^5y^7)/( square root of z)	$\frac{\log_{3} (x^{5} y^{7})}{\sqrt{z}}$
32039	Evaluate	log base 3 of (1/27)^3	$\log_{3} ({(\frac{1}{27})}^{3})$
32040	Evaluate	log base 3 of (1/9)^4	$\log_{3} ({(\frac{1}{9})}^{4})$
32041	Evaluate	( log base 3 of 3/4+ log base 3 of 4/5+ log base 3 of 5/6+ log base 3 of 6/7+ log base 3 of 7/8+ log base 3 of 8/9)/( log of 4/5+ log of 5/6+ log of 6/7 log of 7/8+ log of 8/9+ log of 9/10)	$\frac{\log_{3} (\frac{3}{4}) + \log_{3} (\frac{4}{5}) + \log_{3} (\frac{5}{6}) + \log_{3} (\frac{6}{7}) + \log_{3} (\frac{7}{8}) + \log_{3} (\frac{8}{9})}{\log (\frac{4}{5}) + \log (\frac{5}{6}) + \log (\frac{6}{7}) \log (\frac{7}{8}) + \log (\frac{8}{9}) + \log (\frac{9}{10})}$
32042	Evaluate	log base 3 of ((4x)/(7y))^9	$\log_{3} ({(\frac{4 x}{7 y})}^{9})$
32043	Evaluate	( log base 3 of a^3-3 log base 3 of b)/( log base 9 of ab^-1)	$\frac{\log_{3} (a^{3}) - 3 \log_{3} (b)}{\log_{9} (a b^{- 1})}$
32044	Evaluate	( log base 3 of e^-2)/( log base 3 of e^(-1/3))	$\frac{\log_{3} (e^{- 2})}{\log_{3} (e^{- \frac{1}{3}})}$
32045	Evaluate	log base 3 of (u^2*v)^6	$\log_{3} ({(u^{2} \cdot v)}^{6})$
32046	Evaluate	log base 3 of (115)^3	$\log_{3} ({(115)}^{3})$
32047	Evaluate	( log base 3 of 12)/( log base 3 of e)	$\frac{\log_{3} (12)}{\log_{3} (e)}$
32048	Evaluate	( log base 3 of 20)/2	$\frac{\log_{3} (20)}{2}$
32049	Evaluate	log base 3 of (243)^2	$\log_{3} ({(243)}^{2})$
32050	Evaluate	( log of 1/2)*16	$(\log (\frac{1}{2})) \cdot 16$
32051	Evaluate	-( log of 5+5 log of 7)/(7 log of 5- log of 7)	$- \frac{\log (5) + 5 \log (7)}{7 \log (5) - \log (7)}$
32052	Evaluate	( log base 3 of 7+3)/2	$\frac{\log_{3} (7) + 3}{2}$
32053	Convert to Logarithmic Form	y=e^(-x)	$y = e^{- x}$
32054	Convert to Logarithmic Form	y=x^2	$y = x^{2}$
32055	Convert to Logarithmic Form	y=1.4(1.9)^x	$y = 1.4 {(1.9)}^{x}$
32056	Evaluate	(y-3)^2=12(x-2)	${(y - 3)}^{2} = 12 (x - 2)$
32057	Evaluate	(( natural log of 87)/( natural log of 9)+1)/2	$\frac{\frac{\ln (87)}{\ln (9)} + 1}{2}$
32058	Convert to Logarithmic Form	y=e^(-2x+x^2)	$y = e^{- 2 x + x^{2}}$
32059	Evaluate	log base 2 of (2)^12	$\log_{2} ({(2)}^{12})$
32060	Evaluate	log base 2 of (2)^69	$\log_{2} ({(2)}^{69})$
32061	Evaluate	( log of 12)/( log of 3)	$\frac{\log (12)}{\log (3)}$
32062	Evaluate	( log of 128)/( log of 2)	$\frac{\log (128)}{\log (2)}$
32063	Evaluate	( log of 15)/( log of 2)	$\frac{\log (15)}{\log (2)}$
32064	Evaluate	( log of 15)/( log of 4)	$\frac{\log (15)}{\log (4)}$
32065	Evaluate	( log of 17)/( log of e)	$\frac{\log (17)}{\log (e)}$
32066	Evaluate	( log of 18)/( log of e)	$\frac{\log (18)}{\log (e)}$
32067	Evaluate	( log of 19)/( log of e)	$\frac{\log (19)}{\log (e)}$
32068	Evaluate	( log of 3)/( log of 1/5)	$\frac{\log (3)}{\log (\frac{1}{5})}$
32069	Evaluate	( log of 3)/( log of 0.4)	$\frac{\log (3)}{\log (0.4)}$
32070	Evaluate	( log of 30)/( log of 1/3)	$\frac{\log (30)}{\log (\frac{1}{3})}$
32071	Evaluate	( log of 30)/( log of e)	$\frac{\log (30)}{\log (e)}$
32072	Evaluate	( log of 364)/( log of 14)	$\frac{\log (364)}{\log (14)}$
32073	Evaluate	( log of 5)/( log of 1.03)	$\frac{\log (5)}{\log (1.03)}$
32074	Evaluate	( log of 51)/( log of p)	$\frac{\log (51)}{\log (p)}$
32075	Evaluate	( log of 54)/( log of 9/2)	$\frac{\log (54)}{\log (\frac{9}{2})}$
32076	Evaluate	( log of 61)/( log of e)	$\frac{\log (61)}{\log (e)}$
32077	Evaluate	( log of 63)/( log of p)	$\frac{\log (63)}{\log (p)}$
32078	Evaluate	( log of 8)/( log of 64)	$\frac{\log (8)}{\log (64)}$
32079	Evaluate	( log of 80)/( log of 2)	$\frac{\log (80)}{\log (2)}$
32080	Evaluate	( log of 9)/( log of 1/2)	$\frac{\log (9)}{\log (\frac{1}{2})}$
32081	Evaluate	( log base 11 of 7)/( log base 11 of 4)	$\frac{\log_{11} (7)}{\log_{11} (4)}$
32082	Evaluate	log base 13 of (1/3)^4	$\log_{13} ({(\frac{1}{3})}^{4})$
32083	Evaluate	log base 2 of (1/2)^6	$\log_{2} ({(\frac{1}{2})}^{6})$
32084	Evaluate	log base 2 of (a^2 square root of b)^4	$\log_{2} ({(a^{2} \sqrt{b})}^{4})$
32085	Evaluate	( natural log of 3)/0.024	$\frac{\ln (3)}{0.024}$
32086	Evaluate	(( log of x)^2-( log of y)^2)/( log of xy)	$\frac{\log^{2} (x) - \log^{2} (y)}{\log (x y)}$
32087	Evaluate	(2000^( natural log of 19/10*5))/2	$\frac{2000^{\ln (\frac{19}{10}) \cdot 5}}{2}$
32088	Evaluate	6^( log base 6 of 27)	$6^{\log_{6} (27)}$
32089	Evaluate	( natural log of (1)^2)/0.02	$\frac{\ln ({(1)}^{2})}{0.02}$
32090	Evaluate	(( natural log of 2)/19)/( natural log of 4)	$\frac{\frac{\ln (2)}{19}}{\ln (4)}$
32091	Evaluate	(( natural log of 2)/32)/( natural log of 4)	$\frac{\frac{\ln (2)}{32}}{\ln (4)}$
32092	Evaluate	( natural log of (x-5)^(1/3)(x^2+1)^(3/7))/( natural log of (3x+1)^(4/3)(x^3-1)^(-1/7))	$\frac{\ln ({(x - 5)}^{\frac{1}{3}} {(x^{2} + 1)}^{\frac{3}{7}})}{\ln ({(3 x + 1)}^{\frac{4}{3}} {(x^{3} - 1)}^{- \frac{1}{7}})}$
32093	Evaluate	log of (5/2)^(125/8)	$\log ({(\frac{5}{2})}^{\frac{125}{8}})$
32094	Evaluate	(( log of 21)/( log of 20))/4	$\frac{\frac{\log (21)}{\log (20)}}{4}$
32095	Evaluate	( log of 39)/( log of 6)	$\frac{\log (39)}{\log (6)}$
32096	Evaluate	(( log of 58)/( log of 8))/-5	$\frac{\frac{\log (58)}{\log (8)}}{- 5}$
32097	Evaluate	log of (0.01)^5	$\log ({(0.01)}^{5})$
32098	Evaluate	( log of 0.015625)/( log of 4)	$\frac{\log (0.015625)}{\log (4)}$
32099	Evaluate	( log of 0.28)/( log of 9)	$\frac{\log (0.28)}{\log (9)}$
32100	Evaluate	log of (1/1000)^7	$\log ({(\frac{1}{1000})}^{7})$