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

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

Step 1

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

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

Step 2

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

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

Step 3

Solve for $x$ .

Simplify $2 (3 x - 1)$ .

Start simplifying.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply.

Multiply $3$ by $2$ .

$6 x + 2 \cdot - 1 = 3 x$

Multiply $2$ by $- 1$ .

$6 x - 2 = 3 x$

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

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

$6 x - 2 - 3 x = 0$

Subtract $3 x$ from $6 x$ .

$3 x - 2 = 0$

Add $2$ to both sides of the equation.

$3 x = 2$

Divide each term in $3 x = 2$ by $3$ and simplify.

Divide each term in $3 x = 2$ by $3$ .

$\frac{3 x}{3} = \frac{2}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{2}{3}$

Divide $x$ by $1$ .

$x = \frac{2}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{3}$

Decimal Form:

$x = 0.\overline{6}$