Solve for m 36^(12-m)=6^(2m)

$36^{12 - m} = 6^{2 m}$

Step 1

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

$6^{2 (12 - m)} = 6^{2 m}$

Step 2

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

$2 (12 - m) = 2 m$

Step 3

Solve for $m$ .

Simplify $2 (12 - m)$ .

Rewrite.

$0 + 0 + 2 (12 - m) = 2 m$

Simplify by adding zeros.

$2 (12 - m) = 2 m$

Apply the distributive property.

$2 \cdot 12 + 2 (- m) = 2 m$

Multiply.

Multiply $2$ by $12$ .

$24 + 2 (- m) = 2 m$

Multiply $- 1$ by $2$ .

$24 - 2 m = 2 m$

Move all terms containing $m$ to the left side of the equation.

Subtract $2 m$ from both sides of the equation.

$24 - 2 m - 2 m = 0$

Subtract $2 m$ from $- 2 m$ .

$24 - 4 m = 0$

Subtract $24$ from both sides of the equation.

$- 4 m = - 24$

Divide each term in $- 4 m = - 24$ by $- 4$ and simplify.

Divide each term in $- 4 m = - 24$ by $- 4$ .

$\frac{- 4 m}{- 4} = \frac{- 24}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 m}{- 4} = \frac{- 24}{- 4}$

Divide $m$ by $1$ .

$m = \frac{- 24}{- 4}$

Simplify the right side.

Divide $- 24$ by $- 4$ .

$m = 6$