Hello! For this problem we need to make use of two existing logarithmic properties. These are:
1. [tex]log \frac{M}{N} [/tex] is equal to [tex]log M-logN[/tex]
2. [tex]log(MN) [/tex] is equal to [tex]log M+logN[/tex]
Following the first property, we can simplify the expression to [tex]log \frac{1}{2}-log(8w) [/tex].
Then, we will use the second property to the term 8w. The final form of the expression would then be [tex]log \frac{1}{2}-(log8+logw)[/tex]
ANSWER: [tex]log \frac{1}{2}-(log8+logw)[/tex] (second option)
