Solve for x 64^(3x)=16^(x+2)

$64^{3 x} = 16^{x + 2}$

Step 1

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

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

Step 2

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

$3 (3 x) = 2 (x + 2)$

Step 3

Solve for $x$ .

Multiply $3$ by $3$ .

$9 x = 2 (x + 2)$

Simplify $2 (x + 2)$ .

Apply the distributive property.

$9 x = 2 x + 2 \cdot 2$

Multiply $2$ by $2$ .

$9 x = 2 x + 4$

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

Subtract $2 x$ from both sides of the equation.

$9 x - 2 x = 4$

Subtract $2 x$ from $9 x$ .

$7 x = 4$

Divide each term in $7 x = 4$ by $7$ and simplify.

Divide each term in $7 x = 4$ by $7$ .

$\frac{7 x}{7} = \frac{4}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{4}{7}$

Divide $x$ by $1$ .

$x = \frac{4}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{7}$

Decimal Form:

$x = 0.\overline{571428}$