Solve for x 3^(4x)=9^(x-10)

$3^{4 x} = 9^{x - 10}$

Step 1

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

$3^{4 x} = 3^{2 (x - 10)}$

Step 2

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

$4 x = 2 (x - 10)$

Step 3

Solve for $x$ .

Simplify $2 (x - 10)$ .

Apply the distributive property.

$4 x = 2 x + 2 \cdot - 10$

Multiply $2$ by $- 10$ .

$4 x = 2 x - 20$

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

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

$4 x - 2 x = - 20$

Subtract $2 x$ from $4 x$ .

$2 x = - 20$

Divide each term in $2 x = - 20$ by $2$ and simplify.

Divide each term in $2 x = - 20$ by $2$ .

$\frac{2 x}{2} = \frac{- 20}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 20}{2}$

Divide $x$ by $1$ .

$x = \frac{- 20}{2}$

Simplify the right side.

Divide $- 20$ by $2$ .

$x = - 10$