Solve for x 2^(3x-4)=8^(x-1)

$2^{3 x - 4} = 8^{x - 1}$

Step 1

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

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

Step 2

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

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

Step 3

Solve for $x$ .

Simplify $3 (x - 1)$ .

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply $3$ by $- 1$ .

$3 x - 4 = 3 x - 3$

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

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

$3 x - 4 - 3 x = - 3$

Combine the opposite terms in $3 x - 4 - 3 x$ .

Subtract $3 x$ from $3 x$ .

$0 - 4 = - 3$

Subtract $4$ from $0$ .

$- 4 = - 3$

Since $- 4 \neq - 3$ , there are no solutions.

No solution