Answer
{$\frac{7}{2}$}
Work Step by Step
Step 1: $9^{x-2}=27$
Step 2: $(3^{2})^{x-2}=3^{3}$
Step 3: $3^{2x-4}=3^{3}$
Step 4: $2x-4=3$
Step 5: $2x=3+4$
Step 6: $2x=7$
Step 7: $x=\frac{7}{2}$
Therefore, the solution set is {$\frac{7}{2}$}.