Solve for x 4^(4x)=8

$4^{4 x} = 8$

Step 1

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

$2^{2 (4 x)} = 2^{3}$

Step 2

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

$2 (4 x) = 3$

Step 3

Solve for $x$ .

Multiply $4$ by $2$ .

$8 \cdot x = 3$

Divide each term in $(8 \cdot x) = 3$ by $8$ and simplify.

Divide each term in $(8 \cdot x) = 3$ by $8$ .

$\frac{(8 \cdot x)}{8} = \frac{3}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 \cdot x}{8} = \frac{3}{8}$

Divide $x$ by $1$ .

$x = \frac{3}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{8}$

Decimal Form:

$x = 0.375$