Answer
{$\frac{2}{99}$}
Work Step by Step
Step 1: $\log (x+2)-\log x=2$
Step 2: $\log \frac{x+2}{x}=2$
Step 3: $\frac{x+2}{x}=10^{2}$
Step 4: $\frac{x+2}{x}=100$
Step 5: $x+2=100x$
Step 6: $100x-x=2$
Step 7: $99x=2$
Step 8: $x=\frac{2}{99}$
Step 9: Therefore, the solution set is {$\frac{2}{99}$}
