Solve for m 32=2^(2m-9)

$32 = 2^{2 m - 9}$

Step 1

Rewrite the equation as $2^{2 m - 9} = 32$ .

$2^{2 m - 9} = 32$

Step 2

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

$2^{2 m - 9} = 2^{5}$

Step 3

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

$2 m - 9 = 5$

Step 4

Solve for $m$ .

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

Add $9$ to both sides of the equation.

$2 m = 5 + 9$

Add $5$ and $9$ .

$2 m = 14$

Divide each term in $2 m = 14$ by $2$ and simplify.

Divide each term in $2 m = 14$ by $2$ .

$\frac{2 m}{2} = \frac{14}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 m}{2} = \frac{14}{2}$

Divide $m$ by $1$ .

$m = \frac{14}{2}$

Simplify the right side.

Divide $14$ by $2$ .

$m = 7$