Solve for x 3^(x-2)=81

$3^{x - 2} = 81$

Step 1

Create equivalent expressions in the equation that all have equal bases.

$3^{x - 2} = 3^{4}$

Step 2

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x - 2 = 4$

Step 3

Move all terms not containing $x$ to the right side of the equation.

Add $2$ to both sides of the equation.

$x = 4 + 2$

Add $4$ and $2$ .

$x = 6$