How do you expand #ln(sqrt(((xy^2)/z))#?

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Answer 1 · 2016-05-17T00:45:01

For this problem, we will use the following #ln# properties:

#• ln^a = aln#
#• ln(x/y) = lnx - lny#
#• ln(xy) = lnx + lny#

First, let's establish that #sqrt(a) = a^(1/2)#

Therefore, #ln(sqrt((xy^2)/z)) = ln((xy^2)/z)^(1/2)#

#= 1/2ln((xy^2)/z)#

#= 1/2(lnxy^2 - lnz)#

#= 1/2(lnx + lny^2 - lnz)#

Hopefully this helps!