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simplify ((ln(0.25)+ln(0.5)+ln(0.75))20.5)/2	simplify\:\frac{(\ln(0.25)+\ln(0.5)+\ln(0.75))\cdot\:2\cdot\:0.5}{2}
simplify (3/2)^2*ln(3/2)	simplify\:(\frac{3}{2})^{2}\cdot\:\ln(\frac{3}{2})
expand log_{b}(5)+2log_{b}(2)	expand\:\log_{b}(5)+2\log_{b}(2)
simplify ln(0.26)-ln(0.394)	simplify\:\ln(0.26)-\ln(0.394)
simplify ln(3e)-3ln(3)	simplify\:\ln(3e)-3\ln(3)
simplify 1/2 ln(20)-1/2 ln(8)	simplify\:\frac{1}{2}\ln(20)-\frac{1}{2}\ln(8)
expand ln(3/(x^4y))	expand\:\ln(\frac{3}{x^{4}y})
changebase log_{7}(52)	changebase\:\log_{7}(52)
simplify ln\|x+1\|-1/2 ln\|x^2+1\|+arctan(x)+C	simplify\:\ln\left\|x+1\right\|-\frac{1}{2}\ln\left\|x^{2}+1\right\|+\arctan(x)+C
simplify ln((4x)/(x+1))	simplify\:\ln(\frac{4x}{x+1})
simplify 4.7+log_{10}((0.2)/(0.1))	simplify\:4.7+\log_{10}(\frac{0.2}{0.1})
simplify 3ln\|x-3\|+5ln\|x+2\|+5/9 ln\|2x+3\|	simplify\:3\ln\left\|x-3\right\|+5\ln\left\|x+2\right\|+\frac{5}{9}\ln\left\|2x+3\right\|
simplify log_{10}(a)+4log_{10}(b)-2log_{10}(c)	simplify\:\log_{10}(a)+4\log_{10}(b)-2\log_{10}(c)
expand log_{10}(a/(b^2))	expand\:\log_{10}(\frac{a}{b^{2}})
expand log_{10}(((x^x))/5)	expand\:\log_{10}(\frac{(x^{x})}{5})
expand log_{2}(x/y)	expand\:\log_{2}(\frac{x}{y})
simplify ln((x^6)/(sqrt(x^2-25)))	simplify\:\ln(\frac{x^{6}}{\sqrt{x^{2}-25}})
simplify ln(e^{-θn}(θ))	simplify\:\ln(e^{-θn}(θ))
simplify-log_{10}(1.45*10^{-11})	simplify\:-\log_{10}(1.45\cdot\:10^{-11})
expand log_{3}((x/(y^2))^2)	expand\:\log_{3}((\frac{x}{y^{2}})^{2})
simplify (19.16)/(0.0004600.02)ln(1/(1-0.9))	simplify\:\frac{19.16}{0.0004\cdot\:60\cdot\:0.02}\ln(\frac{1}{1-0.9})
simplify ln(x^2+sqrt(1+x^4))-ln(4+sqrt(17))	simplify\:\ln(x^{2}+\sqrt{1+x^{4}})-\ln(4+\sqrt{17})
simplify 1/(-30)ln(7/12)	simplify\:\frac{1}{-30}\ln(\frac{7}{12})
simplify 100+20*ln((65)/(65-38))	simplify\:100+20\cdot\:\ln(\frac{65}{65-38})
expand log_{10}(3/u)	expand\:\log_{10}(\frac{3}{u})
simplify-ln(2)+ln(1/2)	simplify\:-\ln(2)+\ln(\frac{1}{2})
simplify ln(1.16*2/1)	simplify\:\ln(1.16\cdot\:\frac{2}{1})
simplify ln(-2x+1)-ln(-x+1)	simplify\:\ln(-2x+1)-\ln(-x+1)
simplify ln(10/40)	simplify\:\ln(\frac{10}{40})
simplify 5log_{2}(x)+log_{2}(t)	simplify\:5\log_{2}(x)+\log_{2}(t)
simplify 2log_{6}(x)+4log_{6}(y)	simplify\:2\log_{6}(x)+4\log_{6}(y)
simplify ln((10^{17})/(10^{18)})	simplify\:\ln(\frac{10^{17}}{10^{18}})
simplify-log_{10}(5.5*10^{-14})	simplify\:-\log_{10}(5.5\cdot\:10^{-14})
simplify ln((5-2sqrt(6))/(2-sqrt(3)))	simplify\:\ln(\frac{5-2\sqrt{6}}{2-\sqrt{3}})
simplify 1/2 ln(1/2)-1/2	simplify\:\frac{1}{2}\ln(\frac{1}{2})-\frac{1}{2}
simplify-log_{10}(10^{-14} 1/(5.4*10^{-4)})	simplify\:-\log_{10}(10^{-14}\frac{1}{5.4\cdot\:10^{-4}})
simplify ln(4x^6y^8)	simplify\:\ln(4x^{6}y^{8})
simplify-1/pi ln((sqrt(6))/2)	simplify\:-\frac{1}{π}\ln(\frac{\sqrt{6}}{2})
simplify ln(3/(-1))	simplify\:\ln(\frac{3}{-1})
simplify 0.15log_{10}(1.31)+0.65log_{10}((45.57+176)/(60))	simplify\:0.15\cdot\:\log_{10}(1.31)+0.65\cdot\:\log_{10}(\frac{45.57+176}{60})
simplify log_{e}(x/e)	simplify\:\log_{e}(\frac{x}{e})
simplify ln\|x^2+4\|-2ln(2)	simplify\:\ln\left\|x^{2}+4\right\|-2\ln(2)
simplify 1/2 ln(y/x)	simplify\:\frac{1}{2}\ln(\frac{y}{x})
expand log_{3}((x^2)/y)	expand\:\log_{3}(\frac{x^{2}}{y})
simplify x-1/2 log_{15}(17)+1/2 log_{15}(3)	simplify\:x-\frac{1}{2}\log_{15}(17)+\frac{1}{2}\log_{15}(3)
expand log_{9}((x(x^2+7))/(sqrt(x^2-7)))	expand\:\log_{9}(\frac{x(x^{2}+7)}{\sqrt{x^{2}-7}})
join 9log_{2sqrt(2)}(2)	join\:9\log_{2\sqrt{2}}(2)
simplify-log_{10}(3.2e^{-4})	simplify\:-\log_{10}(3.2e^{-4})
expand log_{e}(((y-1)/3)^2)	expand\:\log_{e}((\frac{y-1}{3})^{2})
simplify 16+4ln(5/3)	simplify\:16+4\ln(\frac{5}{3})
simplify 15+10ln(x)-15ln(y)	simplify\:15+10\ln(x)-15\ln(y)
simplify ln(30/5)	simplify\:\ln(\frac{30}{5})
expand solve(0= 1/2 (2)-1/2 ln(2^{1/2})+c,c)	expand\:solve(0=\frac{1}{2}(2)-\frac{1}{2}\ln(2^{\frac{1}{2}})+c,c)
expand log_{10}((sqrt(y^5))/(z^2x))	expand\:\log_{10}(\frac{\sqrt{y^{5}}}{z^{2}x})
join sqrt(pi/2)\erfi(sqrt(2ln(2)))	join\:\sqrt{\frac{π}{2}}\erfi(\sqrt{2\ln(2)})
simplify 5log_{a}(x)-1/5 log_{a}(z)+3log_{a}(y)	simplify\:5\log_{a}(x)-\frac{1}{5}\log_{a}(z)+3\log_{a}(y)
simplify log_{e}((x^2+4)/(x^2-4))	simplify\:\log_{e}(\frac{x^{2}+4}{x^{2}-4})
simplify ln(3e^x)	simplify\:\ln(3e^{x})
simplify ln(3/81)	simplify\:\ln(\frac{3}{81})
simplify 3.15+log_{10}((1.875)/(0.625))	simplify\:3.15+\log_{10}(\frac{1.875}{0.625})
simplify 1/2 (ln(5)-ln(4))	simplify\:\frac{1}{2}(\ln(5)-\ln(4))
simplify-3ln\|x+2\|+4ln\|x+3\|	simplify\:-3\ln\left\|x+2\right\|+4\ln\left\|x+3\right\|
simplify 20log_{10}(4pi)-20log_{10}(300000)	simplify\:20\log_{10}(4π)-20\log_{10}(300000)
simplify-ln\|x+2\|+2ln\|x-3\|+C	simplify\:-\ln\left\|x+2\right\|+2\ln\left\|x-3\right\|+C
simplify 1log_{10}(0.65)+(1-1)log_{10}(1-0.65)	simplify\:1\cdot\:\log_{10}(0.65)+(1-1)\cdot\:\log_{10}(1-0.65)
simplify ln(x)+ln(y)+2ln(12-x-y)	simplify\:\ln(x)+\ln(y)+2\ln(12-x-y)
simplify ln(x/((x+1)))	simplify\:\ln(\frac{x}{(x+1)})
simplify 2/3 log_{2}(x)+log_{2}(y)	simplify\:\frac{2}{3}\log_{2}(x)+\log_{2}(y)
simplify 89.9(-ln\|0.3+0.2\|+ln\|0.2\|)	simplify\:89.9(-\ln\left\|0.3+0.2\right\|+\ln\left\|0.2\right\|)
simplify (18)/(16pi^2)ln(((16)^2)/(0.03*16pi^2))	simplify\:\frac{18}{16π^{2}}\ln(\frac{(16)^{2}}{0.03\cdot\:16π^{2}})
simplify-4ln(5)+1/3 ln(y)	simplify\:-4\ln(5)+\frac{1}{3}\ln(y)
expand log_{10}(x/5)	expand\:\log_{10}(\frac{x}{5})
simplify ln(((x+2)^6)/(x^5))	simplify\:\ln(\frac{(x+2)^{6}}{x^{5}})
expand ln((3+x)/4)	expand\:\ln(\frac{3+x}{4})
simplify ln(pi(1.63))	simplify\:\ln(π(1.63))
simplify 2log_{e}(e^{2x}sin(x))	simplify\:2\cdot\:\log_{e}(e^{2x}\cdot\:\sin(x))
simplify ln((25-200)/(199-200))	simplify\:\ln(\frac{25-200}{199-200})
simplify (ln(Δx+x)-ln(x))/(Δx)	simplify\:\frac{\ln(Δx+x)-\ln(x)}{Δx}
simplify (1/54)ln(114486/28000)	simplify\:(\frac{1}{54})\ln(\frac{114486}{28000})
simplify ln(θ/(x^{θ+1)})	simplify\:\ln(\frac{θ}{x^{θ+1}})
simplify 2ln(3t)	simplify\:2\ln(3t)
simplify 4log_{5}(x)+3log_{5}(y)-2log_{5}(z)	simplify\:4\log_{5}(x)+3\log_{5}(y)-2\log_{5}(z)
simplify 88.3+10log_{10}(720/480)	simplify\:88.3+10\log_{10}(\frac{720}{480})
simplify 1/2 ln(x)-ln(y)-3ln(z)	simplify\:\frac{1}{2}\ln(x)-\ln(y)-3\ln(z)
simplify ln(1/4 e^{x^2})	simplify\:\ln(\frac{1}{4}e^{x^{2}})
simplify 30^{(30-21.7)/(53-21.7)log_{10}((0.25)/(0.105))+log_{10}(0.0105)}	simplify\:30^{\frac{30-21.7}{53-21.7}\log_{10}(\frac{0.25}{0.105})+\log_{10}(0.0105)}
simplify ln(2λe^{(-2λ)})	simplify\:\ln(2λe^{(-2λ)})
simplify ln(1.3*10^{12})	simplify\:\ln(1.3\cdot\:10^{12})
simplify ln(0.5*e)	simplify\:\ln(0.5\cdot\:e)
simplify 3log_{2}(p)+5log_{2}(q)	simplify\:3\log_{2}(p)+5\log_{2}(q)
simplify log_{10}(((x-6)^2)/((2x)^3))	simplify\:\log_{10}(\frac{(x-6)^{2}}{(2x)^{3}})
simplify 1/2 ln((1+0.919)/(1-0.919))	simplify\:\frac{1}{2}\ln(\frac{1+0.919}{1-0.919})
expand ln((x^5y)^5)	expand\:\ln((x^{5}y)^{5})
simplify 2ln(3)-ln(18)	simplify\:2\ln(3)-\ln(18)
expand log_{b}(yz^2)	expand\:\log_{b}(yz^{2})
simplify ln((e^3)/(13))	simplify\:\ln(\frac{e^{3}}{13})
simplify-log_{10}(1.4*10^{-3})	simplify\:-\log_{10}(1.4\cdot\:10^{-3})
simplify ln(x^xln(x))	simplify\:\ln(x^{x}\ln(x))
simplify ln(5\sqrt[4]{3})	simplify\:\ln(5\sqrt[4]{3})
simplify ln(4/(0.7))	simplify\:\ln(\frac{4}{0.7})

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