Answer
{$\frac{25}{2}$}
Work Step by Step
Step 1: $\log_{5} 2+\log_{5} x=2$
Step 2: $\log_{5} (2\times x)=2$
Step 3: $\log_{5} (2x)=2$
Step 4: $2x=5^{2}$
Step 5: $2x=25$
Step 6: $x=\frac{25}{2}$
Therefore, the solution set is {$\frac{25}{2}$}.