Solve for x 2^(x-7)=32

$2^{x - 7} = 32$

Step 1

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

$2^{x - 7} = 2^{5}$

Step 2

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

$x - 7 = 5$

Step 3

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

Add $7$ to both sides of the equation.

$x = 5 + 7$

Add $5$ and $7$ .

$x = 12$