Solve for x 2^(x+2)=16^x

$2^{x + 2} = 16^{x}$

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

$2^{x + 2} = 2^{4 x}$

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

$x + 2 = 4 x$

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $4 x$ from both sides of the equation.

$x + 2 - 4 x = 0$

Subtract $4 x$ from $x$ .

$- 3 x + 2 = 0$

Subtract $2$ from both sides of the equation.

$- 3 x = - 2$

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

Divide each term in $- 3 x = - 2$ by $- 3$ .

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Dividing two negative values results in a positive value.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{6}$