Solve for x 4^x=128

$4^{x} = 128$

Step 1

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

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

Step 2

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

$2 x = 7$

Step 3

Divide each term in $2 x = 7$ by $2$ and simplify.

Divide each term in $2 x = 7$ by $2$ .

$\frac{2 x}{2} = \frac{7}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{7}{2}$

Divide $x$ by $1$ .

$x = \frac{7}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{2}$

Decimal Form:

$x = 3.5$

Mixed Number Form:

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