Solve for x 256^x=128

$256^{x} = 128$

Step 1

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

$2^{8 x} = 2^{7}$

Step 2

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

$8 x = 7$

Step 3

Divide each term in $8 x = 7$ by $8$ and simplify.

Divide each term in $8 x = 7$ by $8$ .

$\frac{8 x}{8} = \frac{7}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{7}{8}$

Divide $x$ by $1$ .

$x = \frac{7}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{8}$

Decimal Form:

$x = 0.875$