Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
2001	Expand the Logarithmic Expression	log base 2 of (ab)^2	$\log_{2} ({(a b)}^{2})$
2002	Expand the Logarithmic Expression	log base 4 of square root of 10x	$\log_{4} (\sqrt{10 x})$
2003	Expand the Logarithmic Expression	log base 4 of xy^6z^4	$\log_{4} (x y^{6} z^{4})$
2004	Expand the Logarithmic Expression	log base 2 of AB^2	$\log_{2} (A B^{2})$
2005	Expand the Logarithmic Expression	log base 2 of 20	$\log_{2} (20)$
2006	Expand the Logarithmic Expression	log base 3 of 405/x	$\log_{3} (\frac{405}{x})$
2007	Expand the Logarithmic Expression	log base 5 of 5x^2	$\log_{5} (5 x^{2})$
2008	Expand the Logarithmic Expression	log base 5 of x/2	$\log_{5} (\frac{x}{2})$
2009	Expand the Logarithmic Expression	log base 5 of x^2-25	$\log_{5} (x^{2} - 25)$
2010	Expand the Logarithmic Expression	log base 5 of 125/( square root of x+4)	$\log_{5} (\frac{125}{\sqrt{x + 4}})$
2011	Expand the Logarithmic Expression	log base 4 of x(x-9)	$\log_{4} (x (x - 9))$
2012	Expand the Logarithmic Expression	log base 6 of cube root of 36	$\log_{6} (\sqrt[3]{36})$
2013	Expand the Logarithmic Expression	log base 6 of cube root of 6	$\log_{6} (\sqrt[3]{6})$
2014	Expand the Logarithmic Expression	log base 6 of fourth root of 17	$\log_{6} (\sqrt[4]{17})$
2015	Simplify/Condense	log of 14+1/2* log of 3- log of 2	$\log (14) + \frac{1}{2} \cdot \log (3) - \log (2)$
2016	Simplify/Condense	log of x+7 log of y	$\log (x) + 7 \log (y)$
2017	Simplify/Condense	natural log of x^2-4- natural log of x+2	$\ln (x^{2} - 4) - \ln (x + 2)$
2018	Simplify/Condense	natural log of square root of ex	$\ln (\sqrt{e x})$
2019	Simplify/Condense	natural log of x/(x-3)+ natural log of (x+3)/x- natural log of x^2-9	$\ln (\frac{x}{x - 3}) + \ln (\frac{x + 3}{x}) - \ln (x^{2} - 9)$
2020	Simplify/Condense	natural log of e^(2x-1)	$\ln (e^{2 x - 1})$
2021	Simplify/Condense	natural log of e^2x^3	$\ln (e^{2} x^{3})$
2022	Simplify/Condense	natural log of 6/(e^2)	$\ln (\frac{6}{e^{2}})$
2023	Simplify/Condense	6 log base b of q- log base b of r	$6 \log_{b} (q) - \log_{b} (r)$
2024	Simplify/Condense	natural log of z(z-1)^2	$\ln (z) {(z - 1)}^{2}$
2025	Simplify/Condense	log of 1/( square root of 1000)	$\log (\frac{1}{\sqrt{1000}})$
2026	Simplify/Condense	log of 10000x	$\log (10000 x)$
2027	Simplify/Condense	natural log of x+ natural log of 19	$\ln (x) + \ln (19)$
2028	Simplify/Condense	natural log of 5e^3	$\ln (5 e^{3})$
2029	Find Amplitude, Period, and Phase Shift	f(x)=-4sin(pi/7x-pi)-2	$f (x) = - 4 \sin (\frac{π}{7} x - π) - 2$
2030	Convert from Degrees to Radians	-860	$- 860$
2031	Convert from Degrees to Radians	sec(45)	$\sec (45)$
2032	Convert from Degrees to Radians	cos(90)	$\cos (90)$
2033	Convert from Degrees to Radians	134	$134$
2034	Convert from Degrees to Radians	460	$460$
2035	Convert from Degrees to Radians	-53	$- 53$
2036	Convert from Degrees to Radians	56 degrees	$56 °$
2037	Convert from Radians to Degrees	0.6435	$0.6435$
2038	Convert from Radians to Degrees	0.72	$0.72$
2039	Convert from Radians to Degrees	-(13pi)/18	$- \frac{13 π}{18}$
2040	Convert from Radians to Degrees	(14pi)/5	$\frac{14 π}{5}$
2041	Convert from Radians to Degrees	(23pi)/2	$\frac{23 π}{2}$
2042	Convert from Radians to Degrees	6/5	$\frac{6}{5}$
2043	Convert from Radians to Degrees	(7pi)/36	$\frac{7 π}{36}$
2044	Convert from Radians to Degrees	(9pi)/12	$\frac{9 π}{12}$
2045	Convert from Radians to Degrees	-0.32175055	$- 0.3217\overline{50}$
2046	Convert from Radians to Degrees	0.643501108793	$0.64350110$
2047	Convert from Radians to Degrees	0.47	$0.47$
2048	Convert from Radians to Degrees	4.1	$4.1$
2049	Convert from Radians to Degrees	2.2	$2.2$
2050	Convert from Radians to Degrees	0.5	$0.5$
2051	Convert from Radians to Degrees	1.30	$1.3$
2052	Graph	(x^2)/16+(y^2)/6=1	$\frac{x^{2}}{16} + \frac{y^{2}}{6} = 1$
2053	Convert from Degrees to Radians	(5pi)/2	$\frac{5 π}{2}$
2054	Evaluate the Summation	sum from k=3 to 4 of k^2-2k	$\sum_{k = 3}^{4} k^{2} - 2 k$
2055	Evaluate the Summation	sum from k=10 to 60 of 2k	$\sum_{k = 10}^{60} 2 k$
2056	Evaluate the Summation	sum from n=1 to 4 of (3/4)^n	$\sum_{n = 1}^{4} {(\frac{3}{4})}^{n}$
2057	Evaluate the Summation	sum from n=0 to 8 of 1/(6^n)	$\sum_{n = 0}^{8} \frac{1}{6^{n}}$
2058	Evaluate the Summation	sum from i=6 to 12 of -5i+17	$\sum_{i = 6}^{12} - 5 i + 17$
2059	Evaluate the Summation	sum from k=1 to 6 of 9k	$\sum_{k = 1}^{6} 9 k$
2060	Evaluate the Summation	sum from k=1 to 6 of 6k^3	$\sum_{k = 1}^{6} 6 k^{3}$
2061	Evaluate the Summation	sum from K=1 to 7 of -3(2)^(k-1)	$\sum_{K = 1}^{7} - 3 {(2)}^{k - 1}$
2062	Evaluate the Summation	sum from k=1 to 50 of 8	$\sum_{k = 1}^{50} 8$
2063	Evaluate the Summation	sum from k=1 to 25 of k^2	$\sum_{k = 1}^{25} k^{2}$
2064	Evaluate the Summation	sum from k=1 to 4 of (-3/7)^k	$\sum_{k = 1}^{4} {(- \frac{3}{7})}^{k}$
2065	Evaluate the Summation	sum from k=1 to 4 of 7k	$\sum_{k = 1}^{4} 7 k$
2066	Evaluate the Summation	sum from i=1 to 22 of 6i-5	$\sum_{i = 1}^{22} 6 i - 5$
2067	Evaluate the Summation	sum from n=11 to 30 of n	$\sum_{n = 11}^{30} n$
2068	Evaluate the Summation	sum from n=1 to 8 of 5*(1/5)^n	$\sum_{n = 1}^{8} 5 \cdot {(\frac{1}{5})}^{n}$
2069	Evaluate the Summation	sum from n=1 to 8 of (1/5)^(n-1)	$\sum_{n = 1}^{8} {(\frac{1}{5})}^{n - 1}$
2070	Evaluate the Limit	limit as x approaches 8 of (6n^2+5)/(3n^2)	$lim_{x \to 8} \frac{6 n^{2} + 5}{3 n^{2}}$
2071	Evaluate the Limit	limit as x approaches infinity of 3e^(6x)-2	$lim_{x \to \infty} 3 e^{6 x} - 2$
2072	Evaluate the Limit	limit as x approaches 8 of sec(x)	$lim_{x \to 8} \sec (x)$
2073	Evaluate the Limit	limit as x approaches 0 of (5(3x+6))/5*((x+6)(-6x^2-20x-16))	$lim_{x \to 0} \frac{5 (3 x + 6)}{5} \cdot ((x + 6) (- 6 x^{2} - 20 x - 16))$
2074	Evaluate the Limit	limit as x approaches 0 of (1-cos(2x))/(xtan(2x))	$lim_{x \to 0} \frac{1 - \cos (2 x)}{x \tan (2 x)}$
2075	Evaluate the Limit	limit as x approaches 0 of x^2+11	$lim_{x \to 0} x^{2} + 11$
2076	Evaluate the Limit	limit as x approaches 1 of square root of 3x-2	$lim_{x \to 1} \sqrt{3 x - 2}$
2077	Evaluate the Limit	limit as n approaches 8 of 5n^2-15	$lim_{n \to 8} 5 n^{2} - 15$
2078	Evaluate the Limit	limit as x approaches 0 of p	$lim_{x \to 0} p$
2079	Identify the Sequence	0 , 2 , 0 , 2 , 0 , 2	$0$ , $2$ , $0$ , $2$ , $0$ , $2$
2080	Evaluate the Limit	limit as a approaches 25 of ( square root of a-5)/(a-25)	$lim_{a \to 25} \frac{\sqrt{a} - 5}{a - 25}$
2081	Identify the Sequence	2 , 6 , 10 , 14	$2$ , $6$ , $10$ , $14$
2082	Identify the Sequence	2 , 4 , 8 , 16 , 64	$2$ , $4$ , $8$ , $16$ , $64$
2083	Identify the Sequence	2 , -4 , 6 , -8 , 10	$2$ , $- 4$ , $6$ , $- 8$ , $10$
2084	Identify the Sequence	11 , 22 , 44 , 88	$11$ , $22$ , $44$ , $88$
2085	Identify the Sequence	16 , 20 , 24 , 28	$16$ , $20$ , $24$ , $28$
2086	Identify the Sequence	1 , 4 , 7 , 10	$1$ , $4$ , $7$ , $10$
2087	Identify the Sequence	1 , 2 , 4 , 6 , 8	$1$ , $2$ , $4$ , $6$ , $8$
2088	Identify the Sequence	1 , 3 , 5 , 7	$1$ , $3$ , $5$ , $7$
2089	Identify the Sequence	1 , 2 , 4 , 8 , 16	$1$ , $2$ , $4$ , $8$ , $16$
2090	Identify the Sequence	11 , 44 , 176 , 704	$11$ , $44$ , $176$ , $704$
2091	Identify the Sequence	5 , 20 , 80 , 320	$5$ , $20$ , $80$ , $320$
2092	Identify the Sequence	5 , 6 , 7 , 8	$5$ , $6$ , $7$ , $8$
2093	Identify the Sequence	9 , 14 , 19 , 24	$9$ , $14$ , $19$ , $24$
2094	Evaluate the Summation	sum from 1 to 110 of 11	$\sum_{1}^{110} 11$
2095	Evaluate the Summation	sum from 2 to 5 of 6i	$\sum_{2}^{5} 6 i$
2096	Find the Sum of the First @NUM Terms	135 , 45 , 15	$135$ , $45$ , $15$
2097	Evaluate the Summation	sum from i=1 to 3 of 3n-2	$\sum_{i = 1}^{3} 3 n - 2$
2098	Evaluate the Summation	sum from i=1 to 20 of -3i+33	$\sum_{i = 1}^{20} - 3 i + 33$
2099	Evaluate the Summation	sum from i=1 to 15 of -i-6	$\sum_{i = 1}^{15} - i - 6$
2100	Evaluate the Summation	sum from i=1 to 4 of (-1/7)^i	$\sum_{i = 1}^{4} {(- \frac{1}{7})}^{i}$