I got this as a question:

Simplify. State any restrictions on the variables.

$\displaystyle 2 log w + (3/2) log w + (1/2) log w^2$

For this question I did this:

$\displaystyle 2 log w + (3/2) log w + (1/2) log w^2$

$\displaystyle 2 log w + (3/2) log w + (1/2) x 2 log w$

$\displaystyle 2 log w + (3/2) log w + log w$

$\displaystyle 2 log w + (3/2) log w$

$\displaystyle (9/2) log w$

The $\displaystyle 2 log w + log w$ is still 2 log because it is multiplying by one correct and $\displaystyle (1/2) log w^2$ is 1 log because you are multiplying $\displaystyle (1/2)$ by two to get one correct?