Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
40201	Simplify/Condense	log base 2 of 4(a-b)	$\log_{2} (4) (a - b)$
40202	Simplify/Condense	( log base 2 of 4*1)/625	$\frac{\log_{2} (4) \cdot 1}{625}$
40203	Simplify/Condense	2 log of x^5y^4+4 log of x/1-5 log of y	$2 \log (x^{5} y^{4}) + 4 \log (\frac{x}{1}) - 5 \log (y)$
40204	Simplify/Condense	2 log of 1-1	$2 \log (1 - 1)$
40205	Simplify/Condense	2 log of 2x+2 log of 2y-1/2*( log of 2z)	$2 \log (2) x + 2 \log (2) y - \frac{1}{2} \cdot (\log (2) z)$
40206	Simplify/Condense	2 log of 3-1/2* log of x^2+1	$2 \log (3) - \frac{1}{2} \cdot \log (x^{2} + 1)$
40207	Simplify/Condense	2 log of 4*16	$2 \log (4) \cdot 16$
40208	Simplify/Condense	2 log of a-1/3* log of b+ log of c	$2 \log (a) - \frac{1}{3} \cdot \log (b) + \log (c)$
40209	Simplify/Condense	2 log of p*(3 log of q)	$2 \log (p) \cdot (3 \log (q))$
40210	Simplify/Condense	2 log of x+1/3* log of x-2-5 log of 2x+3	$2 \log (x) + \frac{1}{3} \cdot \log (x - 2) - 5 \log (2 x + 3)$
40211	Simplify/Condense	2 log of x+1/3* log of y- log of z-3 log of w	$2 \log (x) + \frac{1}{3} \cdot \log (y) - \log (z) - 3 \log (w)$
40212	Simplify/Condense	2 log of x-1- log of x^2-1	$2 \log (x - 1) - \log (x^{2} - 1)$
40213	Simplify/Condense	2 log of x-3	$2 \log (x - 3)$
40214	Simplify/Condense	3 natural log of x+1+8 natural log of x-1-5 natural log of x	$3 \ln (x + 1) + 8 \ln (x - 1) - 5 \ln (x)$
40215	Simplify/Condense	3( log base 6 of x+3 log base 6 of y-4 log base 6 of z)	$3 (\log_{6} (x) + 3 \log_{6} (y) - 4 \log_{6} (z))$
40216	Simplify/Condense	3* log base 4 of x^2-4* log base 4 of x^-3+2* log base 4 of x	$3 \cdot \log_{4} (x^{2}) - 4 \cdot \log_{4} (x^{- 3}) + 2 \cdot \log_{4} (x)$
40217	Find the Exact Value	cot(-60)	$\cot (- 60)$
40218	Simplify/Condense	3 log base 3 of w-1/3* log base 3 of y+7 log base 3 of x	$3 \log_{3} (w) - \frac{1}{3} \cdot \log_{3} (y) + 7 \log_{3} (x)$
40219	Simplify/Condense	3 log base 4 of x-1/2 log base 4 of 5-2 log base 4 of y	$3 \log_{4} (x - \frac{1}{2}) \log_{4} (5 - 2) \log_{4} (y)$
40220	Simplify/Condense	3 log base 7 of 2	$3 \log_{7} (2)$
40221	Simplify/Condense	3 log base 7 of x+4 log base 7 of x-8	$3 \log_{7} (x) + 4 \log_{7} (x - 8)$
40222	Simplify/Condense	3 log base 8 of y-1/4* log base 8 of x+2 log base 8 of w	$3 \log_{8} (y) - \frac{1}{4} \cdot \log_{8} (x) + 2 \log_{8} (w)$
40223	Simplify/Condense	3 log base b of w-1/3* log base b of z+6 log base b of y	$3 \log_{b} (w) - \frac{1}{3} \cdot \log_{b} (z) + 6 \log_{b} (y)$
40224	Simplify/Condense	3 log base m of 2w+1+1/5* log base m of w+9	$3 \log_{m} (2 w + 1) + \frac{1}{5} \cdot \log_{m} (w + 9)$
40225	Simplify/Condense	3 natural log of e^(x+5)	$3 \ln (e^{x + 5})$
40226	Simplify/Condense	3 natural log of 18	$3 \ln (18)$
40227	Simplify/Condense	3 natural log of 2- natural log of 1/2	$3 \ln (2) - \ln (\frac{1}{2})$
40228	Simplify/Condense	3 natural log of 2e	$3 \ln (2 e)$
40229	Simplify/Condense	2( log of x- log of y)	$2 (\log (x) - \log (y))$
40230	Simplify/Condense	2.5 log of 2	$2.5 \log (2)$
40231	Simplify/Condense	log base b of fourth root of (x^7)/(y^4z^9)	$\log_{b} (\sqrt[4]{\frac{x^{7}}{y^{4} z^{9}}})$
40232	Simplify/Condense	log base x of 1/125	$\log_{x} (\frac{1}{125})$
40233	Simplify/Condense	square root of natural log of 147	$\sqrt{\ln (147)}$
40234	Simplify/Condense	square root of natural log of 150	$\sqrt{\ln (150)}$
40235	Simplify/Condense	fifth root of 64 log of 1	$\sqrt[5]{64} \log (1)$
40236	Simplify/Condense	-1+ log of 4	$- 1 + \log (4)$
40237	Simplify/Condense	10* log of 10^(x/10)*10	$10 \cdot \log (10^{\frac{x}{10}} \cdot 10)$
40238	Simplify/Condense	1000e^(( natural log of 2)/2*4)	$1000 e^{\frac{\ln (2)}{2} \cdot 4}$
40239	Simplify/Condense	10 log of 1/7	$10 \log (\frac{1}{7})$
40240	Simplify/Condense	10 log of 115/(10^-12)	$10 \log (\frac{115}{10^{- 12}})$
40241	Simplify/Condense	10 log of 25/0.75	$10 \log (\frac{25}{0.75})$
40242	Simplify/Condense	10 log of a/(10^-16)-10 log of V/(10^-16)	$10 \log (\frac{a}{10^{- 16}}) - 10 \log (\frac{V}{10^{- 16}})$
40243	Simplify/Condense	10 log of x/1000000	$10 \log (\frac{x}{1000000})$
40244	Simplify/Condense	10 log of 20	$10 \log (20)$
40245	Simplify/Condense	(120( natural log of (x^3)^(1/5)(y^2)^(1/3)))/((16z^5)^(1/4))	$\frac{120 (\ln ({(x^{3})}^{\frac{1}{5}} {(y^{2})}^{\frac{1}{3}}))}{{(16 z^{5})}^{\frac{1}{4}}}$
40246	Simplify/Condense	12 log of 5 fourth root of y	$12 \log (5) \sqrt[4]{y}$
40247	Simplify/Condense	-14 log of 1	$- 14 \log (1)$
40248	Simplify/Condense	2 natural log of 3x+1- natural log of 3x^2-5x-2	$2 \ln (3 x + 1) - \ln (3 x^{2} - 5 x - 2)$
40249	Simplify/Condense	3 natural log of 5- natural log of 2	$3 \ln (5) - \ln (2)$
40250	Simplify/Condense	3 natural log of x(2 natural log of y-4 natural log of x+1)+3 natural log of y	$3 \ln (x) (2 \ln (y) - 4 \ln (x + 1)) + 3 \ln (y)$
40251	Simplify/Condense	3 natural log of x- natural log of y-2	$3 \ln (x) - \ln (y - 2)$
40252	Simplify/Condense	3 natural log of z-1/2* natural log of x+4 natural log of y	$3 \ln (z) - \frac{1}{2} \cdot \ln (x) + 4 \ln (y)$
40253	Simplify/Condense	3 log of 4x^3-1/9* log of 4x+19	$3 \log (4 x^{3}) - \frac{1}{9} \cdot \log (4 x + 19)$
40254	Simplify/Condense	3 log of 4z	$3 \log (4 z)$
40255	Simplify/Condense	3 log of 5u+4 log of 5z	$3 \log (5) u + 4 \log (5) z$
40256	Simplify/Condense	3 log of x-1/4* log of x^2+1+4 log of x-1	$3 \log (x) - \frac{1}{4} \cdot \log (x^{2} + 1) + 4 \log (x - 1)$
40257	Simplify/Condense	3 log of x+ log of (x)^2	$3 \log (x) + \log ({(x)}^{2})$
40258	Simplify/Condense	3 log of x-13 log of y	$3 \log (x) - 13 \log (y)$
40259	Simplify/Condense	3 log of x+1/2 log of y- log of z-4 log of w	$3 \log (x + \frac{1}{2}) \log (y) - \log (z) - 4 \log (w)$
40260	Simplify/Condense	3 log of x+4+2 log of x-7-5 log of x-2+ log of x^2	$3 \log (x + 4) + 2 \log (x - 7) - 5 \log (x - 2) + \log (x^{2})$
40261	Simplify/Condense	3 log of x+y+2 log of x-y- log of x^2+y^2	$3 \log (x + y) + 2 \log (x - y) - \log (x^{2} + y^{2})$
40262	Simplify/Condense	4( log base 3 of x*(4 log base 3 of y)-4 log base 3 of z)	$4 (\log_{3} (x) \cdot (4 \log_{3} (y)) - 4 \log_{3} (z))$
40263	Simplify/Condense	2-2 log of 20	$2 - 2 \log (20)$
40264	Simplify/Condense	24 log base 3 of cube root of x+ log base 3 of 24x^6- log base 3 of 24	$24 \log_{3} (\sqrt[3]{x}) + \log_{3} (24 x^{6}) - \log_{3} (24)$
40265	Simplify/Condense	27 log base 8 of 2	$27 \log_{8} (2)$
40266	Simplify/Condense	29.5+1.4 log of 159+1	$29.5 + 1.4 \log (159 + 1)$
40267	Simplify/Condense	2 natural log of 5-3 natural log of x+ natural log of x^2-10	$2 \ln (5) - 3 \ln (x) + \ln (x^{2} - 10)$
40268	Simplify/Condense	2 natural log of 5- natural log of x- natural log of 29	$2 \ln (5) - \ln (x) - \ln (29)$
40269	Simplify/Condense	4 log base 4 of square root of 4x-3- log base 5 of 2/x+ log base 5 of 2	$4 \log_{4} (\sqrt{4 x - 3}) - \log_{5} (\frac{2}{x}) + \log_{5} (2)$
40270	Simplify/Condense	4 log base 4 of 8-2	$4 \log_{4} (8 - 2)$
40271	Simplify/Condense	4 log base 5 of z-1/2 log base 5 of y+7 log base 5 of x	$4 \log_{5} (z - \frac{1}{2}) \log_{5} (y + 7) \log_{5} (x)$
40272	Simplify/Condense	4 natural log of 2	$4 \ln (2)$
40273	Simplify/Condense	4 natural log of 7-0	$4 \ln (7) - 0$
40274	Evaluate	log base 1/5 of 125	$\log_{\frac{1}{5}} (125)$
40275	Simplify/Condense	4 natural log of x+2-9 natural log of x	$4 \ln (x + 2) - 9 \ln (x)$
40276	Simplify/Condense	4 log of 17.3	$4 \log (17.3)$
40277	Simplify/Condense	4 log of 2	$4 \log (2)$
40278	Simplify/Condense	4 log of 49-x^2-( log of 7+x+ log of 7-x)	$4 \log (49 - x^{2}) - (\log (7 + x) + \log (7 - x))$
40279	Simplify/Condense	4 log of 8w+4 log of 8u+20 log of 8v	$4 \log (8) w + 4 \log (8) u + 20 \log (8) v$
40280	Simplify/Condense	4 log of 8w+4 log of 8u+20 log of 8v	$4 \log (8 w) + 4 \log (8 u) + 20 \log (8 v)$
40281	Simplify/Condense	4 log of x-1/3 log of x^2+1+2 log of x-1	$4 \log (x - \frac{1}{3}) \log (x^{2} + 1) + 2 \log (x - 1)$
40282	Simplify/Condense	4 log of x+6- log of x	$4 \log (x + 6) - \log (x)$
40283	Simplify/Condense	5 log base 3 of x+4 log base 3 of x-3	$5 \log_{3} (x) + 4 \log_{3} (x - 3)$
40284	Simplify/Condense	5 log base 7 of 6y+1+1/(5 log base 7 of y+5)	$5 \log_{7} (6 y + 1) + \frac{1}{5 \log_{7} (y + 5)}$
40285	Find the Roots (Zeros)	f(x)=x^4-45x^2-196	$f (x) = x^{4} - 45 x^{2} - 196$
40286	Simplify/Condense	5 log of y+ log of 8x+5y	$5 \log (y) + \log (8 x + 5 y)$
40287	Simplify/Condense	6 log base 3 of u+3 log base 3 of v	$6 \log_{3} (u) + 3 \log_{3} (v)$
40288	Simplify/Condense	6 log base 6 of z-2-4 log base 6 of z+4	$6 \log_{6} (z - 2) - 4 \log_{6} (z + 4)$
40289	Simplify/Condense	6 log base m of w-1/2* log base m of x+2 log base m of y	$6 \log_{m} (w) - \frac{1}{2} \cdot \log_{m} (x) + 2 \log_{m} (y)$
40290	Simplify/Condense	log base b of 14	$\log_{b} (14)$
40291	Simplify/Condense	log base b of 2y+5-1/2* log base b of y+3	$\log_{b} (2 y + 5) - \frac{1}{2} \cdot \log_{b} (y + 3)$
40292	Find the Asymptotes	(x^2-4)/(x-2)	$\frac{x^{2} - 4}{x - 2}$
40293	Simplify/Condense	log base b of x-1/4 log base b of z+3 log base b of y	$\log_{b} (x - \frac{1}{4}) \log_{b} (z + 3) \log_{b} (y)$
40294	Simplify/Condense	log base b of x+20- log base b of x	$\log_{b} (x + 20) - \log_{b} (x)$
40295	Simplify/Condense	log base c of square root of (x^9)/(y^7z^2)	$\log_{c} (\sqrt{\frac{x^{9}}{y^{7} z^{2}}})$
40296	Simplify/Condense	log base c of seventh root of (x^8)/(y^7z^2)	$\log_{c} (\sqrt[7]{\frac{x^{8}}{y^{7} z^{2}}})$
40297	Find the Asymptotes	(x^2-9)/(x-3)	$\frac{x^{2} - 9}{x - 3}$
40298	Simplify/Condense	-2 log base 8 of 5	$- 2 \log_{8} (5)$
40299	Simplify/Condense	natural log of e^(\|-2x-4\|)	$\ln (e^{\| - 2 x - 4 \|})$
40300	Simplify/Condense	log base h of 2y+5-1/2* log base h of y+3	$\log_{h} (2 y + 5) - \frac{1}{2} \cdot \log_{h} (y + 3)$