Solve for x 4^(x+35)=64^(x-3)

$4^{x + 35} = 64^{x - 3}$

Step 1

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

$4^{x + 35} = 4^{3 (x - 3)}$

Step 2

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

$x + 35 = 3 (x - 3)$

Step 3

Solve for $x$ .

Simplify $3 (x - 3)$ .

Rewrite.

$x + 35 = 0 + 0 + 3 (x - 3)$

Simplify by adding zeros.

$x + 35 = 3 (x - 3)$

Apply the distributive property.

$x + 35 = 3 x + 3 \cdot - 3$

Multiply $3$ by $- 3$ .

$x + 35 = 3 x - 9$

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

Subtract $3 x$ from both sides of the equation.

$x + 35 - 3 x = - 9$

Subtract $3 x$ from $x$ .

$- 2 x + 35 = - 9$

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

Subtract $35$ from both sides of the equation.

$- 2 x = - 9 - 35$

Subtract $35$ from $- 9$ .

$- 2 x = - 44$

Divide each term in $- 2 x = - 44$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 44$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 44}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 44}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 44}{- 2}$

Simplify the right side.

Divide $- 44$ by $- 2$ .

$x = 22$