3^(x-2)=81

1 answer

To solve the equation \( 3^{(x - 2)} = 81 \), we first express 81 as a power of 3.

We know that:

\[ 81 = 3^4 \]

Now 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 \( x \):

\[ x = 4 + 2 = 6 \]

Therefore, the solution is:

\[ \boxed{6} \]