Solve for x solve 3^(x-2)=3^7

solve $3^{x - 2} = 3^{7}$

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

$3^{x - 2} = 3^{7}$

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

$x - 2 = 7$

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

Add $2$ to both sides of the equation.

$x = 7 + 2$

Add $7$ and $2$ .

$x = 9$