To answer this question we will use the following property of logarithms:
[tex]\log a-\log b=\log \frac{a}{b}\text{.}[/tex]Therefore:
[tex]\log 500-\log \frac{1}{2}=\log \frac{500}{\frac{1}{2}}\text{.}[/tex]Simplifying the above result we get:
[tex]\log \frac{500}{\frac{1}{2}}=\log (500\cdot2)=\log 1000.[/tex]Now, notice that:
[tex]1000=10^3\text{.}[/tex]Therefore:
[tex]\log 1000=3.[/tex]Answer:
[tex]\log 500-\log \frac{1}{2}=3.[/tex]