Solve the following equation: 3^(x−2)=81

. What is the missing value? (1 point)

1 answer

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 \( \boxed{6} \).