Solve for n 2^(3n)=4

$2^{3 n} = 4$

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

$2^{3 n} = 2^{2}$

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

$3 n = 2$

Divide each term in $3 n = 2$ by $3$ and simplify.

Divide each term in $3 n = 2$ by $3$ .

$\frac{3 n}{3} = \frac{2}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 n}{3} = \frac{2}{3}$

Divide $n$ by $1$ .

$n = \frac{2}{3}$

The result can be shown in multiple forms.

Exact Form:

$n = \frac{2}{3}$

Decimal Form:

$n = 0.\overline{6}$