Evaluate 8^(x-1)=2^(x+2)

$8^{x - 1} = 2^{x + 2}$

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

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

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

$3 (x - 1) = x + 2$

Solve for $x$ .

Simplify $3 (x - 1)$ .

Rewrite.

$0 + 0 + 3 (x - 1) = x + 2$

Simplify by adding zeros.

$3 (x - 1) = x + 2$

Apply the distributive property.

$3 x + 3 \cdot - 1 = x + 2$

Multiply $3$ by $- 1$ .

$3 x - 3 = x + 2$

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

Subtract $x$ from both sides of the equation.

$3 x - 3 - x = 2$

Subtract $x$ from $3 x$ .

$2 x - 3 = 2$

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

Add $3$ to both sides of the equation.

$2 x = 2 + 3$

Add $2$ and $3$ .

$2 x = 5$

Divide each term in $2 x = 5$ by $2$ and simplify.

Divide each term in $2 x = 5$ by $2$ .

$\frac{2 x}{2} = \frac{5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{5}{2}$

Divide $x$ by $1$ .

$x = \frac{5}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{2}$

Decimal Form:

$x = 2.5$

Mixed Number Form:

$x = 2 \frac{1}{2}$