Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
22601	Simplify/Condense	6 log of a+18 log of b	$6 \log (a) + 18 \log (b)$
22602	Simplify/Condense	6 log of x+4 log of x+6	$6 \log (x) + 4 \log (x + 6)$
22603	Simplify/Condense	6 log of x+6 log of y	$6 \log (x) + 6 \log (y)$
22604	Simplify/Condense	6 log of x-6 log of y	$6 \log (x) - 6 \log (y)$
22605	Simplify/Condense	7( log of x- log of y)	$7 (\log (x) - \log (y))$
22606	Graph	r=3csc(theta+90)	$r = 3 \csc (θ + 90)$
22607	Simplify/Condense	7*(10 log of 10^7)	$7 \cdot (10 \log (10^{7}))$
22608	Simplify/Condense	6 natural log of 3.3+2 natural log of 1.5	$6 \ln (3.3) + 2 \ln (1.5)$
22609	Simplify/Condense	6 natural log of e+4 natural log of 1-9 natural log of 3 square root of e+ natural log of e^4	$6 \ln (e) + 4 \ln (1) - 9 \ln (3 \sqrt{e}) + \ln (e^{4})$
22610	Simplify/Condense	6 natural log of PQ- natural log of P/Q	$6 \ln (P Q) - \ln (\frac{P}{Q})$
22611	Simplify/Condense	6 natural log of x-1/2* natural log of x^2+3	$6 \ln (x) - \frac{1}{2} \cdot \ln (x^{2} + 3)$
22612	Simplify/Condense	6 natural log of x-1/6* natural log of y	$6 \ln (x) - \frac{1}{6} \cdot \ln (y)$
22613	Simplify/Condense	(6 natural log of x1)/7 natural log of y	$\frac{6 \ln (x) \cdot 1}{7} \cdot \ln (y)$
22614	Simplify/Condense	6 natural log of x-1/8* natural log of y	$6 \ln (x) - \frac{1}{8} \cdot \ln (y)$
22615	Simplify/Condense	6 natural log of x+2 natural log of y-4 natural log of 2	$6 \ln (x) + 2 \ln (y) - 4 \ln (2)$
22616	Simplify/Condense	6 natural log of x+2 natural log of y-4 natural log of z	$6 \ln (x) + 2 \ln (y) - 4 \ln (z)$
22617	Simplify/Condense	6 natural log of x+3 natural log of y-5 natural log of z	$6 \ln (x) + 3 \ln (y) - 5 \ln (z)$
22618	Simplify/Condense	6 natural log of x-3 natural log of y+ natural log of z	$6 \ln (x) - 3 \ln (y) + \ln (z)$
22619	Simplify/Condense	6 natural log of x+7-4 natural log of x	$6 \ln (x + 7) - 4 \ln (x)$
22620	Simplify/Condense	6 log base 5 of square root of 7x-8- log base 5 of 3/x+ log base 5 of 3	$6 \log_{5} (\sqrt{7 x - 8}) - \log_{5} (\frac{3}{x}) + \log_{5} (3)$
22621	Simplify/Condense	6 log base 5 of 5x- log base 5 of x^6	$6 \log_{5} (5 x) - \log_{5} (x^{6})$
22622	Simplify/Condense	6 log base 5 of w+( log base 5 of u)/2+( log base 5 of v)/2	$6 \log_{5} (w) + \frac{\log_{5} (u)}{2} + \frac{\log_{5} (v)}{2}$
22623	Simplify/Condense	6 log base 5 of x+12 log base 5 of y	$6 \log_{5} (x) + 12 \log_{5} (y)$
22624	Simplify/Condense	6 log base 6 of 10-24 log base 6 of 3	$6 \log_{6} (10) - 24 \log_{6} (3)$
22625	Simplify/Condense	6 log base 6 of 36	$6 \log_{6} (36)$
22626	Simplify/Condense	6 log base 6 of 3y+1+1/4* log base 6 of y+2	$6 \log_{6} (3 y + 1) + \frac{1}{4} \cdot \log_{6} (y + 2)$
22627	Simplify/Condense	6 log base 7 of square root of 3x-7- log base 7 of 3/x+ log base 7 of 3	$6 \log_{7} (\sqrt{3 x - 7}) - \log_{7} (\frac{3}{x}) + \log_{7} (3)$
22628	Simplify/Condense	6 log base 7 of square root of 6x-7- log base 7 of 4/x+ log base 7 of 4	$6 \log_{7} (\sqrt{6 x - 7}) - \log_{7} (\frac{4}{x}) + \log_{7} (4)$
22629	Simplify/Condense	6 log base 7 of 8y+1+1/4* log base 7 of y+9	$6 \log_{7} (8 y + 1) + \frac{1}{4} \cdot \log_{7} (y + 9)$
22630	Simplify/Condense	6 log base 7 of u+9 log base 7 of v	$6 \log_{7} (u) + 9 \log_{7} (v)$
22631	Simplify/Condense	6 log base 8 of x+1/4* log base 8 of y	$6 \log_{8} (x) + \frac{1}{4} \cdot \log_{8} (y)$
22632	Simplify/Condense	6 log base 8 of x+8 log base 8 of y-2 log base 8 of z	$6 \log_{8} (x) + 8 \log_{8} (y) - 2 \log_{8} (z)$
22633	Simplify/Condense	6 log base 9 of cube root of y	$6 \log_{9} (\sqrt[3]{y})$
22634	Simplify/Condense	6 log base 9 of x- log base 9 of z-2 log base 9 of y	$6 \log_{9} (x) - \log_{9} (z) - 2 \log_{9} (y)$
22635	Simplify/Condense	6 log base a of x-5-4 log base a of x+2	$6 \log_{a} (x - 5) - 4 \log_{a} (x + 2)$
22636	Simplify/Condense	6 log base b of 4x^3-1/3* log base b of 4x+9	$6 \log_{b} (4 x^{3}) - \frac{1}{3} \cdot \log_{b} (4 x + 9)$
22637	Simplify/Condense	6 natural log of 3x^4-1/5 natural log of 3x+7	$6 \ln (3 x^{4} - \frac{1}{5}) \ln (3 x + 7)$
22638	Simplify/Condense	6-2.5 log of (7.5*10^-2)/(10^-6)	$6 - 2.5 \log (\frac{7.5 \cdot 10^{- 2}}{10^{- 6}})$
22639	Simplify/Condense	62+35* log of x-4	$62 + 35 \cdot \log (x - 4)$
22640	Simplify/Condense	62+35 log of 12-4	$62 + 35 \log (12 - 4)$
22641	Simplify/Condense	6 log base 4 of z-1/5* log base 4 of y+7 log base 4 of x	$6 \log_{4} (z) - \frac{1}{5} \cdot \log_{4} (y) + 7 \log_{4} (x)$
22642	Simplify/Condense	5 natural log of x+8-7 natural log of x	$5 \ln (x + 8) - 7 \ln (x)$
22643	Simplify/Condense	5 natural log of x-2 natural log of x-7 natural log of z+21 natural log of w	$5 \ln (x) - 2 \ln (x) - 7 \ln (z) + 21 \ln (w)$
22644	Simplify/Condense	3 log of 3	$3 \log (3)$
22645	Simplify/Condense	3 log of 3*(2x)	$3 \log (3) \cdot (2 x)$
22646	Simplify/Condense	3 log of 3*7	$3 \log (3) \cdot 7$
22647	Simplify/Condense	3 log of 4+5 log of x-2 log of 3- log of y	$3 \log (4) + 5 \log (x) - 2 \log (3) - \log (y)$
22648	Simplify/Condense	3 log of 4+ log of 6- log of 8	$3 \log (4) + \log (6) - \log (8)$
22649	Simplify/Condense	3 log of 4- log of 8+4 log of 2-2 log of 8	$3 \log (4) - \log (8) + 4 \log (2) - 2 \log (8)$
22650	Simplify/Condense	3 log of 5(x+5)- log of 5(x-19)- log of 5(x-8)	$3 \log (5) (x + 5) - \log (5) (x - 19) - \log (5) (x - 8)$
22651	Simplify/Condense	3 log of 6	$3 \log (6)$
22652	Simplify/Condense	3 log of 6x+5 log of 6(x-6)	$3 \log (6) x + 5 \log (6) (x - 6)$
22653	Simplify/Condense	3 log of k-2 log of q	$3 \log (k) - 2 \log (q)$
22654	Simplify/Condense	3 log of m+2 log of n+ log of p	$3 \log (m) + 2 \log (n) + \log (p)$
22655	Simplify/Condense	3 log of (y^4)/x-2 log of y+1/2* log of x^6y^8	$3 \log (\frac{y^{4}}{x}) - 2 \log (y) + \frac{1}{2} \cdot \log (x^{6} y^{8})$
22656	Simplify/Condense	3 log of 9/( square root of x+3)	$3 \log (\frac{9}{\sqrt{x + 3}})$
22657	Simplify/Condense	3 log of x^3y^4+5 log of 1/x-5 log of y	$3 \log (x^{3} y^{4}) + 5 \log (\frac{1}{x}) - 5 \log (y)$
22658	Simplify/Condense	3 log of x^3y^4+5 log of 1/x-3 log of y	$3 \log (x^{3} y^{4}) + 5 \log (\frac{1}{x}) - 3 \log (y)$
22659	Simplify/Condense	3 log of x^4y^3+3 log of 1/x-8 log of y	$3 \log (x^{4} y^{3}) + 3 \log (\frac{1}{x}) - 8 \log (y)$
22660	Simplify/Condense	3 log of x^4y^3*(3 log of 1/x)-4 log of y	$3 \log (x^{4} y^{3}) \cdot (3 \log (\frac{1}{x})) - 4 \log (y)$
22661	Simplify/Condense	3 log of 100- log of 1000	$3 \log (100) - \log (1000)$
22662	Simplify/Condense	3 log of 2-1/2* log of 16	$3 \log (2) - \frac{1}{2} \cdot \log (16)$
22663	Simplify/Condense	3 log of 2+3 log of 3	$3 \log (2) + 3 \log (3)$
22664	Simplify/Condense	-3 log of 2x	$- 3 \log (2 x)$
22665	Simplify/Condense	3 natural log of x+2-4 natural log of x+1/2* natural log of x-3	$3 \ln (x + 2) - 4 \ln (x) + \frac{1}{2} \cdot \ln (x - 3)$
22666	Simplify/Condense	3 natural log of x+4+7 natural log of y-2 natural log of x+1	$3 \ln (x + 4) + 7 \ln (y) - 2 \ln (x + 1)$
22667	Simplify/Condense	3 natural log of x+4 natural log of y-5 natural log of z	$3 \ln (x + 4) \ln (y - 5) \ln (z)$
22668	Simplify/Condense	3 natural log of x+5 natural log of y-4 natural log of z	$3 \ln (x) + 5 \ln (y) - 4 \ln (z)$
22669	Simplify/Condense	3 natural log of x+6 natural log of y-2 natural log of z	$3 \ln (x) + 6 \ln (y) - 2 \ln (z)$
22670	Simplify/Condense	3 natural log of x+6 natural log of y-4 natural log of z	$3 \ln (x) + 6 \ln (y) - 4 \ln (z)$
22671	Simplify/Condense	3 natural log of x-2 natural log of 7	$3 \ln (x) - 2 \ln (7)$
22672	Simplify/Condense	3 natural log of x-2 natural log of x+2 natural log of x	$3 \ln (x) - 2 \ln (x) + 2 \ln (x)$
22673	Simplify/Condense	4( natural log of z+ natural log of z+7)-2 natural log of z-7	$4 (\ln (z) + \ln (z + 7)) - 2 \ln (z - 7)$
22674	Simplify/Condense	4e^(10 natural log of a)	$4 e^{10 \ln (a)}$
22675	Simplify/Condense	(4( natural log of y))/( natural log of 10)+(2( natural log of x))/( natural log of 10)	$\frac{4 (\ln (y))}{\ln (10)} + \frac{2 (\ln (x))}{\ln (10)}$
22676	Simplify/Condense	4 log of (1/93)^2- log of 1/93+5	$4 \log ({(\frac{1}{9} \cdot 3)}^{2}) - \log (\frac{1}{9}) \cdot 3 + 5$
22677	Simplify/Condense	4-( log of 89)/( log of 3)	$4 - \frac{\log (89)}{\log (3)}$
22678	Simplify/Condense	4 log of x-2 log of y	$4 \log (x) - 2 \log (y)$
22679	Simplify/Condense	4 log base 2 of 4- log base 2 of 8	$4 \log_{2} (4) - \log_{2} (8)$
22680	Simplify/Condense	4 log base 2 of x	$4 \log_{2} (x)$
22681	Simplify/Condense	4 log base 2 of x-7-6 log base 2 of x+3	$4 \log_{2} (x - 7) - 6 \log_{2} (x + 3)$
22682	Simplify/Condense	4 log base 3 of 27^x	$4 \log_{3} (27^{x})$
22683	Simplify/Condense	4 log base 3 of A-1/2* log base 3 of B	$4 \log_{3} (A) - \frac{1}{2} \cdot \log_{3} (B)$
22684	Simplify/Condense	4 log base 3 of a*(3 log base 3 of 2b)- log base 3 of m	$4 \log_{3} (a) \cdot (3 \log_{3} (2 b)) - \log_{3} (m)$
22685	Simplify/Condense	4 log base 3 of x+24 log base 3 of y	$4 \log_{3} (x) + 24 \log_{3} (y)$
22686	Simplify/Condense	4 log base 3 of x-20 log base 3 of y	$4 \log_{3} (x) - 20 \log_{3} (y)$
22687	Simplify/Condense	4 log base 3 of x-8 log base 3 of y- log base 3 of 2	$4 \log_{3} (x) - 8 \log_{3} (y) - \log_{3} (2)$
22688	Simplify/Condense	4 log base 3 of x+3- log base 3 of x-2- log base 3 of x-6	$4 \log_{3} (x + 3) - \log_{3} (x - 2) - \log_{3} (x - 6)$
22689	Simplify/Condense	4 log base 3 of x-1	$4 \log_{3} (x - 1)$
22690	Simplify/Condense	4 log base 3 of y+3 log base 3 of x	$4 \log_{3} (y) + 3 \log_{3} (x)$
22691	Simplify/Condense	4 log base 3 of y-4-3 log base 3 of y+4 log base 3 of x	$4 \log_{3} (y - 4) - 3 \log_{3} (y + 4) \log_{3} (x)$
22692	Simplify/Condense	4 log base 3 of z-1/4* log base 3 of x+7 log base 3 of 7	$4 \log_{3} (z) - \frac{1}{4} \cdot \log_{3} (x) + 7 \log_{3} (7)$
22693	Simplify/Condense	4 log base 4 of 12-4 log base 16 of 2	$4 \log_{4} (12) - 4 \log_{16} (2)$
22694	Simplify/Condense	4 log base 4 of 2+1/7* log base 4 of x-9-1/2* log base 4 of x	$4 \log_{4} (2) + \frac{1}{7} \cdot \log_{4} (x - 9) - \frac{1}{2} \cdot \log_{4} (x)$
22695	Simplify/Condense	4 log base 4 of 2+1/7 log base 4 of r-7-1/2* log base 4 of r	$4 \log_{4} (2 + \frac{1}{7}) \log_{4} (r - 7) - \frac{1}{2} \cdot \log_{4} (r)$
22696	Simplify/Condense	4 log base 4 of x-3 log base 4 of y+2 log base 4 of z	$4 \log_{4} (x) - 3 \log_{4} (y) + 2 \log_{4} (z)$
22697	Simplify/Condense	4 log base 4 of x+8	$4 \log_{4} (x + 8)$
22698	Simplify/Condense	4 log base 4 of y-1/3 log base 4 of x+3 log base 4 of w	$4 \log_{4} (y - \frac{1}{3}) \log_{4} (x) + 3 \log_{4} (w)$
22699	Simplify/Condense	4 log base 5 of 7x+1+0.5 log base 5 of x+3	$4 \log_{5} (7 x + 1) + 0.5 \log_{5} (x + 3)$
22700	Simplify/Condense	4 log base 5 of u+2 log base 5 of v	$4 \log_{5} (u) + 2 \log_{5} (v)$