I have the expression

. In simplifying the first term I need to get rid of the square root and change the coefficient of 4 to an exponent. So if I get rid of the square root first that would be

so when I now change the coefficient of 4 to an exponent, shouldnt the term be

? It seems that the actual answer is

but according to the properties of logarithms I dont understand why. The properties say that

and

so why is the simplification of the term

and not

?

In other words if

then why am I simply multiplying the exponent of 1/2 in

by 4 instead of raising it to a power of 4?