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

$8^{- \frac{x}{3}} = 4$

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

$2^{3 (- \frac{x}{3})} = 2^{2}$

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

$3 (- \frac{x}{3}) = 2$

Solve for $x$ .

Simplify.

Multiply $- 1$ by $3$ .

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

Combine $- 3$ and $\frac{x}{3}$ .

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

Divide each term in $\frac{- 3 x}{3} = 2$ by $- 3$ and simplify.

Divide each term in $\frac{- 3 x}{3} = 2$ by $- 3$ .

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

Simplify the left side.

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

Factor $3$ out of $- 3 x$ .

$\frac{\frac{3 (- x)}{3}}{- 3} = \frac{2}{- 3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{\frac{3 (- x)}{3 (1)}}{- 3} = \frac{2}{- 3}$

Cancel the common factor.

$\frac{\frac{3 (- x)}{3 \cdot 1}}{- 3} = \frac{2}{- 3}$

Rewrite the expression.

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

Divide $- x$ by $1$ .

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

Dividing two negative values results in a positive value.

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

Simplify the right side.

Move the negative in front of the fraction.

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

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x = - 2$