Solve for x 8^(x+3)=16^(x-1)

$8^{x + 3} = 16^{x - 1}$

Step 1

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

$2^{3 (x + 3)} = 2^{4 (x - 1)}$

Step 2

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

$3 (x + 3) = 4 (x - 1)$

Step 3

Solve for $x$ .

Simplify $3 (x + 3)$ .

Rewrite.

$0 + 0 + 3 (x + 3) = 4 (x - 1)$

Simplify by adding zeros.

$3 (x + 3) = 4 (x - 1)$

Apply the distributive property.

$3 x + 3 \cdot 3 = 4 (x - 1)$

Multiply $3$ by $3$ .

$3 x + 9 = 4 (x - 1)$

Simplify $4 (x - 1)$ .

Apply the distributive property.

$3 x + 9 = 4 x + 4 \cdot - 1$

Multiply $4$ by $- 1$ .

$3 x + 9 = 4 x - 4$

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

Subtract $4 x$ from both sides of the equation.

$3 x + 9 - 4 x = - 4$

Subtract $4 x$ from $3 x$ .

$- x + 9 = - 4$

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

Subtract $9$ from both sides of the equation.

$- x = - 4 - 9$

Subtract $9$ from $- 4$ .

$- x = - 13$

Divide each term in $- x = - 13$ by $- 1$ and simplify.

Divide each term in $- x = - 13$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 13}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 13}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 13}{- 1}$

Simplify the right side.

Divide $- 13$ by $- 1$ .

$x = 13$