Solve for x 36^(x-9)=6^(2x)

$36^{x - 9} = 6^{2 x}$

Step 1

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

$6^{2 (x - 9)} = 6^{2 x}$

Step 2

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

$2 (x - 9) = 2 x$

Step 3

Solve for $x$ .

Simplify $2 (x - 9)$ .

Rewrite.

$0 + 0 + 2 (x - 9) = 2 x$

Simplify by adding zeros.

$2 (x - 9) = 2 x$

Apply the distributive property.

$2 x + 2 \cdot - 9 = 2 x$

Multiply $2$ by $- 9$ .

$2 x - 18 = 2 x$

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

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

$2 x - 18 - 2 x = 0$

Combine the opposite terms in $2 x - 18 - 2 x$ .

Subtract $2 x$ from $2 x$ .

$0 - 18 = 0$

Subtract $18$ from $0$ .

$- 18 = 0$

Since $- 18 \neq 0$ , there are no solutions.

No solution