Solve for x 16^(3x-6)=64^(x+4)

$16^{3 x - 6} = 64^{x + 4}$

Step 1

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

$4^{2 (3 x - 6)} = 4^{3 (x + 4)}$

Step 2

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

$2 (3 x - 6) = 3 (x + 4)$

Step 3

Solve for $x$ .

Simplify $2 (3 x - 6)$ .

Rewrite.

$0 + 0 + 2 (3 x - 6) = 3 (x + 4)$

Simplify by adding zeros.

$2 (3 x - 6) = 3 (x + 4)$

Apply the distributive property.

$2 (3 x) + 2 \cdot - 6 = 3 (x + 4)$

Multiply.

Multiply $3$ by $2$ .

$6 x + 2 \cdot - 6 = 3 (x + 4)$

Multiply $2$ by $- 6$ .

$6 x - 12 = 3 (x + 4)$

Simplify $3 (x + 4)$ .

Apply the distributive property.

$6 x - 12 = 3 x + 3 \cdot 4$

Multiply $3$ by $4$ .

$6 x - 12 = 3 x + 12$

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

Subtract $3 x$ from both sides of the equation.

$6 x - 12 - 3 x = 12$

Subtract $3 x$ from $6 x$ .

$3 x - 12 = 12$

Move all terms not containing $x$ to the right side of the equation.

Add $12$ to both sides of the equation.

$3 x = 12 + 12$

Add $12$ and $12$ .

$3 x = 24$

Divide each term in $3 x = 24$ by $3$ and simplify.

Divide each term in $3 x = 24$ by $3$ .

$\frac{3 x}{3} = \frac{24}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{24}{3}$

Divide $x$ by $1$ .

$x = \frac{24}{3}$

Simplify the right side.

Divide $24$ by $3$ .

$x = 8$

Solve for x 16^(3x-6)=64^(x+4)

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