How do you expand #ln( sqrt(x^4)/sqrt( y^5))#?

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How do you expand #ln( sqrt(x^4)/sqrt( y^5))#?

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Answer 1 · 2016-03-22T19:16:26

#ln (sqrt(x^4)/sqrt(y^5))##=2lnx-5/2 ln y#

Explanation:

#ln (sqrt(x^4)/sqrt(y^5))#
#=ln(x^4)^(1/2) - ln(y^5)^(1/2)#-> use property #log_n(x/y)=log_b x -log_b y#
#=ln x^2-lny^(5/2)#
#=2lnx-5/2 ln y#-> use property #log_bx^n=n*log_b x#

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How do you expand #ln( sqrt(x^4)/sqrt( y^5))#?

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