Solve for x 16^(5x)=64^(x+7)

$16^{5 x} = 64^{x + 7}$

Step 1

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

$4^{2 (5 x)} = 4^{3 (x + 7)}$

Step 2

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

$2 (5 x) = 3 (x + 7)$

Step 3

Solve for $x$ .

Multiply $5$ by $2$ .

$10 x = 3 (x + 7)$

Simplify $3 (x + 7)$ .

Apply the distributive property.

$10 x = 3 x + 3 \cdot 7$

Multiply $3$ by $7$ .

$10 x = 3 x + 21$

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

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

$10 x - 3 x = 21$

Subtract $3 x$ from $10 x$ .

$7 x = 21$

Divide each term in $7 x = 21$ by $7$ and simplify.

Divide each term in $7 x = 21$ by $7$ .

$\frac{7 x}{7} = \frac{21}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{21}{7}$

Divide $x$ by $1$ .

$x = \frac{21}{7}$

Simplify the right side.

Divide $21$ by $7$ .

$x = 3$