Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
38901	Expand the Logarithmic Expression	log base 2 of (x^6*y)^2	$\log_{2} ({(x^{6} \cdot y)}^{2})$
38902	Expand the Logarithmic Expression	log base 2 of (16)^23	$\log_{2} ({(16)}^{23})$
38903	Expand the Logarithmic Expression	( log base 2 of 16- log of p)/( log base 2 of ( square root of 2)^(8- log of 0.0001))	$\frac{\log_{2} (16 - \log (p))}{\log_{2} ({(\sqrt{2})}^{8 - \log (0.0001)})}$
38904	Expand the Logarithmic Expression	log base 2 of (2)^-13	$\log_{2} ({(2)}^{- 13})$
38905	Expand the Logarithmic Expression	log base 2 of (2)^51	$\log_{2} ({(2)}^{51})$
38906	Expand the Logarithmic Expression	log base 2 of (2)^69	$\log_{2} ({(2)}^{69})$
38907	Expand the Logarithmic Expression	( log base 2 of 200)/( log base 2 of 2b)	$\frac{\log_{2} (200)}{\log_{2} (2 b)}$
38908	Simplify/Condense	log of 6+ log of 5	$\log (6) + \log (5)$
38909	Simplify/Condense	log of 6+ log of 8- log of 3	$\log (6) + \log (8) - \log (3)$
38910	Simplify/Condense	log of 6+x log of 4+ log of 32+4^x	$\log (6) + x \log (4) + \log (32 + 4^{x})$
38911	Simplify/Condense	log of 1000000- log of 1000	$\log (1000000) - \log (1000)$
38912	Find the Directrix	y^2=12x	$y^{2} = 12 x$
38913	Simplify/Condense	log of 12-0.125	$\log (12) - 0.125$
38914	Simplify/Condense	log of 1000x^4	$\log (1000) x^{4}$
38915	Simplify/Condense	log of 1000*32	$\log (1000) \cdot 32$
38916	Add	1/3+1/9+1/27+1/81	$\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{81}$
38917	Simplify/Condense	log of log of (10000)^10000	$\log (\log ({(10000)}^{10000}))$
38918	Simplify/Condense	log of 15 log of 14	$\log (15) \log (14)$
38919	Simplify/Condense	log of 16*1	$\log (16) \cdot 1$
38920	Simplify/Condense	log of 16x	$\log (16 x)$
38921	Simplify/Condense	log of 2((15 square root of r)/s)	$\log (2) (\frac{15 \sqrt{r}}{s})$
38922	Simplify/Condense	log of 2*64	$\log (2) \cdot 64$
38923	Simplify/Condense	log of 2.91	$\log (2.91)$
38924	Simplify/Condense	1/5* log base c of y+3 log base c of z- log base c of x	$\frac{1}{5} \cdot \log_{c} (y) + 3 \log_{c} (z) - \log_{c} (x)$
38925	Simplify/Condense	log of 28+1/2* log of 6- log of 4	$\log (28) + \frac{1}{2} \cdot \log (6) - \log (4)$
38926	Simplify/Condense	log of 3((x-4)/(x^6))	$\log (3) (\frac{x - 4}{x^{6}})$
38927	Simplify/Condense	log of 3(3)	$\log (3) (3)$
38928	Simplify/Condense	log of 3*3^71	$\log (3) \cdot 3^{71}$
38929	Simplify/Condense	log of 3*(11p^3)	$\log (3) \cdot (11 p^{3})$
38930	Simplify/Condense	log of 3*243	$\log (3) \cdot 243$
38931	Simplify/Condense	log of 3x+ log of 3y	$\log (3) x + \log (3) y$
38932	Simplify/Condense	log of 3.2x*10^-14	$\log (3.2 x \cdot 10^{- 14})$
38933	Simplify/Condense	log of 3 fifth root of 81	$\log (3 \sqrt[5]{81})$
38934	Simplify/Condense	( log of 30*1)/900	$\frac{\log (30) \cdot 1}{900}$
38935	Simplify/Condense	log of 32- log base 16 of 1/2	$\log (32) - \log_{16} (\frac{1}{2})$
38936	Simplify/Condense	log of 3z=2	$\log (3 z) = 2$
38937	Simplify/Condense	( log of 4*1)/256	$\frac{\log (4) \cdot 1}{256}$
38938	Simplify/Condense	log of 4*(12x)	$\log (4) \cdot (12 x)$
38939	Simplify/Condense	log of 4- log of 3+ log of p+3 log of r	$\log (4) - \log (3) + \log (p) + 3 \log (r)$
38940	Simplify/Condense	log of 48x^4 cube root of y	$\log (48 x^{4} \sqrt[3]{y})$
38941	Simplify/Condense	log of 5(16)	$\log (5) (16)$
38942	Simplify/Condense	log of 5*10- log of 5m	$\log (5) \cdot 10 - \log (5 m)$
38943	Simplify/Condense	log of 512- log of 53	$\log (5) \cdot 12 - \log (5) \cdot 3$
38944	Simplify/Condense	log of 5x^2	$\log (5 x^{2})$
38945	Simplify/Condense	log of 502*8	$\log (502) \cdot 8$
38946	Simplify/Condense	log of 513+ log of 56	$\log (513) + \log (56)$
38947	Simplify/Condense	log of 6+2 log of 4+ log of 32+4^x	$\log (6) + 2 \log (4) + \log (32 + 4^{x})$
38948	Simplify/Condense	log of 6 fifth root of (s^(6t))/36	$\log (6 \sqrt[5]{\frac{s^{6 t}}{36}})$
38949	Simplify/Condense	log of 7*7^3	$\log (7) \cdot 7^{3}$
38950	Simplify/Condense	log of 713+ log of 710	$\log (7) \cdot 13 + \log (7) \cdot 10$
38951	Simplify/Condense	log of 70000000	$\log (70000000)$
38952	Simplify/Condense	( log of 8*7)/9z	$\frac{\log (8) \cdot 7}{9} z$
38953	Simplify/Condense	log of 80	$\log (80)$
38954	Simplify/Condense	log of 826	$\log (826)$
38955	Simplify/Condense	log of 8x-3 log of 2- log of x	$\log (8 x) - 3 \log (2) - \log (x)$
38956	Simplify/Condense	log of 9+1/3* log of 729	$\log (9) + \frac{1}{3} \cdot \log (729)$
38957	Simplify/Condense	8( log base z of p- log base z of q)-(1/3* log base z of u-3-4 log base z of v)	$8 (\log_{z} (p) - \log_{z} (q)) - (\frac{1}{3} \cdot \log_{z} (u - 3) - 4 \log_{z} (v))$
38958	Simplify/Condense	log of a+ log of 1-2 log of b	$\log (a) + \log (1 - 2) \log (b)$
38959	Simplify/Condense	log of a+ log of 1-2 log of b	$\log (a) + \log (1 - 2 \log (b))$
38960	Simplify/Condense	log of a+1-2b	$\log (a + 1 - 2 b)$
38961	Simplify/Condense	log of b square root of (x^4)/(y^3z)	$\log (b) \sqrt{\frac{x^{4}}{y^{3} z}}$
38962	Simplify/Condense	x log base b of r+ log base b of s- log base b of t	$x \log_{b} (r) + \log_{b} (s) - \log_{b} (t)$
38963	Simplify/Condense	log of z- log of 11y	$\log (z) - \log (11 y)$
38964	Simplify/Condense	x natural log of x=x	$x \ln (x) = x$
38965	Expand the Logarithmic Expression	log base 7 of (xy)^5	$\log_{7} ({(x y)}^{5})$
38966	Expand the Logarithmic Expression	(1/3) natural log of xy	$(\frac{1}{3}) \ln (x y)$
38967	Expand the Logarithmic Expression	(5/2)(sec(2 square root of x)^2+ natural log of cos(2 square root of x))	$(\frac{5}{2}) (\sec^{2} (2 \sqrt{x}) + \ln (\cos (2 \sqrt{x})))$
38968	Expand the Logarithmic Expression	( natural log of 3.7)/(3 natural log of 6)	$\frac{\ln (3.7)}{3 \ln (6)}$
38969	Expand the Logarithmic Expression	( log of x)(3x-1)	$(\log (x)) (3 x - 1)$
38970	Expand the Logarithmic Expression	( log base 2 of 5)( log base 5 of 7)	$(\log_{2} (5)) (\log_{5} (7))$
38971	Expand the Logarithmic Expression	(3 log of 381)( log of 216)	$(3 \log (3) \cdot 81) (\log (2) \cdot 16)$
38972	Expand the Logarithmic Expression	(5+2) log of q+yb	$(5 + 2) \log (q + y) b$
38973	Expand the Logarithmic Expression	( natural log of 5^-3)( natural log of 2/9)^3	$(\ln (5^{- 3})) \ln^{3} (\frac{2}{9})$
38974	Expand the Logarithmic Expression	( natural log of x)(-(x^-8)/8)	$(\ln (x)) (- \frac{x^{- 8}}{8})$
38975	Expand the Logarithmic Expression	( log of x-cos(x))(pi)	$(\log (x) - \cos (x)) (π)$
38976	Expand the Logarithmic Expression	(x+1) log of 3	$(x + 1) \log (3)$
38977	Expand the Logarithmic Expression	0.5(4 natural log of x+4- natural log of x- natural log of x^2-64)	$0.5 (4 \ln (x + 4) - \ln (x) - \ln (x^{2} - 64))$
38978	Expand the Logarithmic Expression	2 log base 7 of x+4+7 log base 7 of x+6-1/2* log base 7 of x	$2 \log_{7} (x + 4) + 7 \log_{7} (x + 6) - \frac{1}{2} \cdot \log_{7} (x)$
38979	Expand the Logarithmic Expression	(3 log of 4(x+6)+3 log of 4(x+4))(-1/2) log of 4x	$(3 \log (4) (x + 6) + 3 \log (4) (x + 4)) (- \frac{1}{2}) \log (4) x$
38980	Simplify/Condense	- log of 1.58*10^6	$- \log (1.58 \cdot 10^{6})$
38981	Simplify/Condense	log of 1(4)(x-1)- log of 1(4)1/x- log of 1(4)	$\log (1 (4)) (x - 1) - \log (1 (4)) \frac{1}{x} - \log (1 (4))$
38982	Simplify/Condense	log of 10(x^2-81)-4 log of 10(x+9)+5 log of 10(x)	$\log (10) (x^{2} - 81) - 4 \log (10) (x + 9) + 5 \log (10 (x))$
38983	Simplify/Condense	log of 10*145	$\log (10) \cdot 145$
38984	Simplify/Condense	log of square root of 1000000s	$\log (\sqrt{1000000 s})$
38985	Simplify/Condense	log of square root of 100t	$\log (\sqrt{100 t})$
38986	Simplify/Condense	log of square root of 5x-9	$\log (\sqrt{5 x - 9})$
38987	Simplify/Condense	log of square root of x+4 log of x- log of 7x^2	$\log (\sqrt{x}) + 4 \log (x) - \log (7 x^{2})$
38988	Simplify/Condense	log of cube root of a^2+ log of cube root of b- log of cube root of c	$\log (\sqrt[3]{a^{2}}) + \log (\sqrt[3]{b}) - \log (\sqrt[3]{c})$
38989	Simplify/Condense	log of ninth root of x/z	$\log (\sqrt[9]{\frac{x}{z}})$
38990	Simplify/Condense	log of x/( cube root of 1-x)	$\log (\frac{x}{\sqrt[3]{1 - x}})$
38991	Simplify/Condense	log of x^2y^5	$\log (x^{2} y^{5})$
38992	Simplify/Condense	log of x^2+3x-18- log of x^2-36	$\log (x^{2} + 3 x - 18) - \log (x^{2} - 36)$
38993	Simplify/Condense	log of a^2-10a-11- log of a^2-1	$\log (a^{2} - 10 a - 11) - \log (a^{2} - 1)$
38994	Simplify/Condense	log of x^2-4- log of x^2+9x+14	$\log (x^{2} - 4) - \log (x^{2} + 9 x + 14)$
38995	Simplify/Condense	log of xz^2	$\log (x z^{2})$
38996	Simplify/Condense	log of z/(y^9)	$\log (\frac{z}{y^{9}})$
38997	Simplify/Condense	log base 5 of 9- log base 5 of 11	$\log_{5} (9) - \log_{5} (11)$
38998	Simplify/Condense	log of 0.000001	$\log (0.000001)$
38999	Simplify/Condense	log of square root of (x^9+7)/((x^8+5)(x^5-10)^4)	$\log (\sqrt{\frac{x^{9} + 7}{(x^{8} + 5) {(x^{5} - 10)}^{4}}})$
39000	Simplify/Condense	log of square root of b^5c	$\log (\sqrt{b^{5} c})$