How do you expand #ln sqrt(x^3/y^2)#?

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Answer 1 · 2016-07-26T16:36:50

#3/2*ln x - lny#

#ln sqrt(x^3/y^2)# can be rewritten as

#ln (x^3/y^2)^(1/2)#

or #ln (x^(3/2)/y^(2/2))#

using one of logarithm rules: #ln (a/b) = lna - lnb#

we have:

#ln x^(3/2) - ln y^(2/2)#

or #ln x^(3/2) - ln y#

another one of these rules state that: #ln a^b = b*lna#

then we have:

#3/2*ln x - lny#