Evaluate 36^(2x-7)=6^(x-5)

$36^{2 x - 7} = 6^{x - 5}$

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

$6^{2 (2 x - 7)} = 6^{x - 5}$

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

$2 (2 x - 7) = x - 5$

Solve for $x$ .

Simplify $2 (2 x - 7)$ .

Rewrite.

$0 + 0 + 2 (2 x - 7) = x - 5$

Simplify by adding zeros.

$2 (2 x - 7) = x - 5$

Apply the distributive property.

$2 (2 x) + 2 \cdot - 7 = x - 5$

Multiply.

Multiply $2$ by $2$ .

$4 x + 2 \cdot - 7 = x - 5$

Multiply $2$ by $- 7$ .

$4 x - 14 = x - 5$

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

Subtract $x$ from both sides of the equation.

$4 x - 14 - x = - 5$

Subtract $x$ from $4 x$ .

$3 x - 14 = - 5$

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

Add $14$ to both sides of the equation.

$3 x = - 5 + 14$

Add $- 5$ and $14$ .

$3 x = 9$

Divide each term in $3 x = 9$ by $3$ and simplify.

Divide each term in $3 x = 9$ by $3$ .

$\frac{3 x}{3} = \frac{9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{9}{3}$

Divide $x$ by $1$ .

$x = \frac{9}{3}$

Simplify the right side.

Divide $9$ by $3$ .

$x = 3$