Solve for x 8^(x-1)=2^(3x+8)

$8^{x - 1} = 2^{3 x + 8}$

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

$2^{3 (x - 1)} = 2^{3 x + 8}$

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

$3 (x - 1) = 3 x + 8$

Solve for $x$ .

Simplify $3 (x - 1)$ .

Rewrite.

$0 + 0 + 3 (x - 1) = 3 x + 8$

Simplify by adding zeros.

$3 (x - 1) = 3 x + 8$

Apply the distributive property.

$3 x + 3 \cdot - 1 = 3 x + 8$

Multiply $3$ by $- 1$ .

$3 x - 3 = 3 x + 8$

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

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

$3 x - 3 - 3 x = 8$

Combine the opposite terms in $3 x - 3 - 3 x$ .

Subtract $3 x$ from $3 x$ .

$0 - 3 = 8$

Subtract $3$ from $0$ .

$- 3 = 8$

Since $- 3 \neq 8$ , there are no solutions.

No solution