Solve for x 4^(8-3x)=256

$4^{8 - 3 x} = 256$

Step 1

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

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

Step 2

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

$8 - 3 x = 4$

Step 3

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Subtract $8$ from both sides of the equation.

$- 3 x = 4 - 8$

Subtract $8$ from $4$ .

$- 3 x = - 4$

Divide each term in $- 3 x = - 4$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 4$ by $- 3$ .

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{4}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{3}$

Decimal Form:

$x = 1.\overline{3}$

Mixed Number Form:

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