Question 153014
4th root is the same as to the 1/4 power. We take powers out of logarithms as fraction coefficients.

So {{{In ^4sqrt(ab^2)}}}=1/4(ln ab^2)
Now, multiplied variables/numbers in logarithms can be taken out as addition.
So (1/4)(ln ab^2)=(1/4)(ln a)+(1/4)(ln b^2)
Now, repeat the first step for the logarithm with b^2.
So (1/4)(ln a)+(1/2)(ln b)