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simplify ln(4e^{2β}x^2)	simplify\:\ln(4e^{2β}x^{2})
simplify ln((x+1)5^x)	simplify\:\ln((x+1)5^{x})
join 4ln(cos((x-7)/4))	join\:4\ln(\cos(\frac{x-7}{4}))
expand log_{8}(xyz^3)	expand\:\log_{8}(x\cdot\:y\cdot\:z^{3})
expand ln((\sqrt[3]{e^2z})/(sqrt(x-3)))	expand\:\ln(\frac{\sqrt[3]{e^{2}z}}{\sqrt{x-3}})
simplify-ln(5)+2ln(2)	simplify\:-\ln(5)+2\ln(2)
simplify 7ln(x+2)-5ln(x)	simplify\:7\ln(x+2)-5\ln(x)
simplify 1/2 (ln(2)-ln(7))	simplify\:\frac{1}{2}(\ln(2)-\ln(7))
simplify ln^2(x)+ln(x^2)	simplify\:\ln^{2}(x)+\ln(x^{2})
simplify ln(P)-ln(1-P)	simplify\:\ln(P)-\ln(1-P)
simplify 2(ln(e^5-1)-ln(e^3-1)-2)	simplify\:2(\ln(e^{5}-1)-\ln(e^{3}-1)-2)
simplify ln((e^4+2e^2)/(1+2e^2))	simplify\:\ln(\frac{e^{4}+2e^{2}}{1+2e^{2}})
simplify 5ln(9/8)+1.5ln(13/9)+3ln(14/13)	simplify\:5\ln(\frac{9}{8})+1.5\ln(\frac{13}{9})+3\ln(\frac{14}{13})
simplify (ln(c(t))-ln(c))e^{rt}	simplify\:(\ln(c(t))-\ln(c))e^{rt}
simplify ln(5*10^{12-4})	simplify\:\ln(5\cdot\:10^{12-4})
simplify log_{10}((5^9)/(\sqrt[3]{-)9*5})	simplify\:\log_{10}(\frac{5^{9}}{\sqrt[3]{-}9\cdot\:5})
simplify 59.7ln(173/285)	simplify\:59.7\ln(\frac{173}{285})
simplify (8(ln\|x+3\|-ln\|x+4\|))/x	simplify\:\frac{8(\ln\left\|x+3\right\|-\ln\left\|x+4\right\|)}{x}
simplify log_{10}(x+2)-2log_{10}(x)	simplify\:\log_{10}(x+2)-2\log_{10}(x)
simplify-4ln(3/4)	simplify\:-4\ln(\frac{3}{4})
simplify 3log_{5}(u)-3log_{5}(v)	simplify\:3\log_{5}(u)-3\log_{5}(v)
simplify log_{10}((1/((1+cot^2(x))^1))/2)	simplify\:\log_{10}(\frac{\frac{1}{(1+\cot^{2}(x))^{1}}}{2})
simplify ln(1/40)	simplify\:\ln(\frac{1}{40})
simplify ln(23138/1500)	simplify\:\ln(\frac{23138}{1500})
simplify 2(ln((x-25)/(25)+1)-ln((x-25)/(25)-1))	simplify\:2(\ln(\frac{x-25}{25}+1)-\ln(\frac{x-25}{25}-1))
simplify ln(40)-ln(400)	simplify\:\ln(40)-\ln(400)
simplify ln((x-1)/x)+c	simplify\:\ln(\frac{x-1}{x})+c
simplify 2+3log_{10}(x)-1/2 log_{10}(x+7)	simplify\:2+3\log_{10}(x)-\frac{1}{2}\log_{10}(x+7)
expand log_{a}((y^5w^2)/(x^4z^3))	expand\:\log_{a}(\frac{y^{5}w^{2}}{x^{4}z^{3}})
simplify ln(1/((r-1)!)θ^{-r}x^{(r-1)}e^{(-xθ-1)})	simplify\:\ln(\frac{1}{(r-1)!}θ^{-r}x^{(r-1)}e^{(-xθ-1)})
simplify ln(4)+4ln(3)	simplify\:\ln(4)+4\ln(3)
simplify-ln(x)+2ln(x+1)	simplify\:-\ln(x)+2\ln(x+1)
simplify ln(b/x)+ln(a/x)	simplify\:\ln(\frac{b}{x})+\ln(\frac{a}{x})
simplify ln(x-3)+ln(x+5)-2ln(x)	simplify\:\ln(x-3)+\ln(x+5)-2\ln(x)
simplify ln(e^{5x+9})-4ln^{3x+6}(x)	simplify\:\ln(e^{5x+9})-4\ln^{3x+6}(x)
simplify 4-2ln((sqrt(2)+1)/(sqrt(2-1)))	simplify\:4-2\ln(\frac{\sqrt{2}+1}{\sqrt{2-1}})
join 25log_{2}(1+10sqrt(10))	join\:25\log_{2}(1+10\sqrt{10})
expand log_{x}((4x+1)^3)	expand\:\log_{x}((4x+1)^{3})
simplify ((ln(1080999)-ln(847595)))/(20)	simplify\:\frac{(\ln(1080999)-\ln(847595))}{20}
simplify log_{10}(2)-log_{10}(1.26)	simplify\:\log_{10}(2)-\log_{10}(1.26)
expand log_{4}(x^4*sqrt(y))	expand\:\log_{4}(x^{4}\cdot\:\sqrt{y})
simplify 3log_{10}(x+2)-log_{10}(2x-3)	simplify\:3\log_{10}(x+2)-\log_{10}(2x-3)
simplify ln((ab)/(\sqrt[3]{x)})	simplify\:\ln(\frac{ab}{\sqrt[3]{x}})
simplify ln((x^2sqrt(x^2+4))/((x+4)^5))	simplify\:\ln(\frac{x^{2}\sqrt{x^{2}+4}}{(x+4)^{5}})
simplify (1/54)ln(65467/29)	simplify\:(\frac{1}{54})\ln(\frac{65467}{29})
simplify log_{5}(1/10000)	simplify\:\log_{5}(\frac{1}{10000})
simplify ln(2x^{5x})	simplify\:\ln(2x^{5x})
simplify 1/(e^{2(ln\|s+100\|-2ln(10)))}	simplify\:\frac{1}{e^{2(\ln\left\|s+100\right\|-2\ln(10))}}
simplify-ln(3/2)+ln(5/3)	simplify\:-\ln(\frac{3}{2})+\ln(\frac{5}{3})
simplify ln(1000/100)	simplify\:\ln(\frac{1000}{100})
simplify ln(7x)-ln(1)	simplify\:\ln(7x)-\ln(1)
simplify-log_{10}(7.21*10^{-6})	simplify\:-\log_{10}(7.21\cdot\:10^{-6})
simplify-1/2 ln(x+1)+2ln(x+2)-3/2 ln(x+3)	simplify\:-\frac{1}{2}\ln(x+1)+2\ln(x+2)-\frac{3}{2}\ln(x+3)
simplify ln(3)(-1-1/2+1/8+3/4)+ln(2)(1-1/4-3/4)	simplify\:\ln(3)(-1-\frac{1}{2}+\frac{1}{8}+\frac{3}{4})+\ln(2)(1-\frac{1}{4}-\frac{3}{4})
simplify 4ln(2y)+2ln(y)	simplify\:4\ln(2y)+2\ln(y)
simplify ln(2\|ln(x)\|)	simplify\:\ln(2\left\|\ln(x)\right\|)
simplify ln(330/293)	simplify\:\ln(\frac{330}{293})
simplify (530)ln(((25))/(30))	simplify\:(5\cdot\:30)\ln(\frac{(2\cdot\:5)}{30})
join 1/3 log_{5}(6)	join\:\frac{1}{3}\log_{5}(6)
simplify 1/2 ln(x)+3ln(5)	simplify\:\frac{1}{2}\ln(x)+3\ln(5)
simplify 20log_{10}(p/(2*10^{-4)})	simplify\:20\log_{10}(\frac{p}{2\cdot\:10^{-4}})
simplify 2000ln((14000)/(14000-2100(1)))-9.8(1)	simplify\:2000\ln(\frac{14000}{14000-2100(1)})-9.8(1)
simplify ln((tan^2(x))/(e^{4x^2)\|x^5\|})	simplify\:\ln(\frac{\tan^{2}(x)}{e^{4x^{2}}\left\|x^{5}\right\|})
simplify ln(e^{-9θ}(θ^9)/(9!))	simplify\:\ln(e^{-9θ}\frac{θ^{9}}{9!})
simplify 1/2 ln(x)+3ln(2)	simplify\:\frac{1}{2}\ln(x)+3\ln(2)
simplify ln(p^4)+ln(3p^5)-2ln(x)	simplify\:\ln(p^{4})+\ln(3p^{5})-2\ln(x)
simplify 3(14/3)-14ln(7(14/3))	simplify\:3(\frac{14}{3})-14\ln(7(\frac{14}{3}))
simplify ln(k*C^a)	simplify\:\ln(k\cdot\:C^{a})
simplify 6ln(x)+1/2 ln(y)-5	simplify\:6\ln(x)+\frac{1}{2}\ln(y)-5
join-(9ln(3/5))/(2pilf)	join\:-\frac{9\ln(\frac{3}{5})}{2πlf}
simplify ln((\|5.1-2\|^2)/(\|5.1-3\|))	simplify\:\ln(\frac{\left\|5.1-2\right\|^{2}}{\left\|5.1-3\right\|})
simplify ln((16)/(x^2))	simplify\:\ln(\frac{16}{x^{2}})
join 3/2*ln(6)	join\:\frac{3}{2}\cdot\:\ln(6)
simplify ln(1/(3^x))	simplify\:\ln(\frac{1}{3^{x}})
simplify 2log_{10}(a)+log_{10}(b)-3log_{10}(c)	simplify\:2\log_{10}(a)+\log_{10}(b)-3\log_{10}(c)
simplify-log_{10}(6.8*10^{-6})	simplify\:-\log_{10}(6.8\cdot\:10^{-6})
d/(du)((t)(ln(t^2)+2ln(t)+2))	\frac{d}{du}((t)(\ln(t^{2})+2\ln(t)+2))
simplify ln((1+0.85)/(1-85))	simplify\:\ln(\frac{1+0.85}{1-85})
simplify 1/3 ln\|f^7(x)\|+29/21 ln\|f(x)+15\|+C	simplify\:\frac{1}{3}\ln\left\|f^{7}(x)\right\|+\frac{29}{21}\ln\left\|f(x)+15\right\|+C
simplify 0.6log_{2}(0.6)+0.4log_{2}(0.4)	simplify\:0.6\cdot\:\log_{2}(0.6)+0.4\cdot\:\log_{2}(0.4)
simplify ln(3)+5ln(x)-ln(y)	simplify\:\ln(3)+5\ln(x)-\ln(y)
simplify ln((sqrt(x^2+1)-x)/(sqrt(x^2-1)+x))	simplify\:\ln(\frac{\sqrt{x^{2}+1}-x}{\sqrt{x^{2}-1}+x})
simplify 0.5(-3/5 log_{2}(3/5)-2/5 log_{2}(2/5))	simplify\:0.5(-\frac{3}{5}\log_{2}(\frac{3}{5})-\frac{2}{5}\log_{2}(\frac{2}{5}))
simplify ln(6)+ln(18)-ln(3)+3ln(6)	simplify\:\ln(6)+\ln(18)-\ln(3)+3\ln(6)
simplify ln(100/5)	simplify\:\ln(\frac{100}{5})
simplify 100+20*ln((65)/(65-30))	simplify\:100+20\cdot\:\ln(\frac{65}{65-30})
simplify 1/4 log_{10}(x)-1/4 log_{10}(y)	simplify\:\frac{1}{4}\log_{10}(x)-\frac{1}{4}\log_{10}(y)
simplify log_{10}(3x-1)+log_{10}(x-1)	simplify\:\log_{10}(3x-1)+\log_{10}(x-1)
expand log_{6}((((xy)^6)/z)^4)	expand\:\log_{6}((\frac{(xy)^{6}}{z})^{4})
simplify ln((e^{4x})/(x^2+1))	simplify\:\ln(\frac{e^{4x}}{x^{2}+1})
simplify ln(6.56*10^{-4})	simplify\:\ln(6.56\cdot\:10^{-4})
simplify ln(6)+ln(sqrt((e^{(2.29928)))/3})	simplify\:\ln(6)+\ln(\sqrt{\frac{e^{(2.29928)}}{3}})
expand log_{2}(8^7)	expand\:\log_{2}(8^{7})
simplify-1/(0.71)ln((0.23)/(0.72))	simplify\:-\frac{1}{0.71}\ln(\frac{0.23}{0.72})
simplify 28log_{10}(x)+log_{10}(y)-27log_{10}(z)	simplify\:28\log_{10}(x)+\log_{10}(y)-27\log_{10}(z)
simplify 10log_{10}((320*10^{-7})/(10^{-12)})	simplify\:10\log_{10}(\frac{320\cdot\:10^{-7}}{10^{-12}})
simplify 2ln(3)+ln(3^2+2)	simplify\:2\ln(3)+\ln(3^{2}+2)
simplify log_{a}(5sqrt(a)xa^4x^3sqrt(a))	simplify\:\log_{a}(5\sqrt{a}xa^{4}x^{3}\sqrt{a})
simplify 10ln((50)/(10^{-12)})	simplify\:10\ln(\frac{50}{10^{-12}})
simplify 7ln(9x)	simplify\:7\ln(9x)

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