ln differentiation question

Quote:

Originally Posted by fran1942

Hello, I am stuck trying to solve this problem.
Can someone please show me the steps so I can understand the procedure.

loge((x+2)^2(x-1)^3)

Thanks kindly for any help.

Simplify using logarithm rules first

$\displaystyle \begin{align*} \ln{ \left[ \left( x + 2 \right) ^2 \left( x - 1 \right) ^3 \right] } &= \ln{ \left( x + 2 \right) ^2 } + \ln{ \left( x - 1 \right) ^3} \\ &= 2\ln{ \left( x + 2 \right)} + 3\ln{ \left( x - 1 \right) } \end{align*}$

I'd say this looks much easier to differentiate...