To solve the equation \( 3^{(x-2)} = 81 \), we can first express 81 as a power of 3.
Since \( 81 = 3^4 \), we can rewrite the equation:
\[ 3^{(x-2)} = 3^4 \]
Since the bases are the same, we can set the exponents equal to each other:
\[ x - 2 = 4 \]
Now, solve for \( x \) by adding 2 to both sides:
\[ x = 4 + 2 \] \[ x = 6 \]
Thus, the missing value is \( \boxed{6} \).