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

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

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

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

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

$3 x = 3 (1 - x)$

Solve for $x$ .

Simplify $3 (1 - x)$ .

Apply the distributive property.

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

Multiply.

Multiply $3$ by $1$ .

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

Multiply $- 1$ by $3$ .

$3 x = 3 - 3 x$

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

Add $3 x$ to both sides of the equation.

$3 x + 3 x = 3$

Add $3 x$ and $3 x$ .

$6 x = 3$

Divide each term in $6 x = 3$ by $6$ and simplify.

Divide each term in $6 x = 3$ by $6$ .

$\frac{6 x}{6} = \frac{3}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{3}{6}$

Divide $x$ by $1$ .

$x = \frac{3}{6}$

Simplify the right side.

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

$x = \frac{3 (1)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$x = \frac{3 \cdot 1}{3 \cdot 2}$

Cancel the common factor.

$x = \frac{3 \cdot 1}{3 \cdot 2}$

Rewrite the expression.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.5$