Solve for c 32^(2c)=8^(c+7)

$32^{2 c} = 8^{c + 7}$

Step 1

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

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

Step 2

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

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

Step 3

Solve for $c$ .

Multiply $2$ by $5$ .

$10 c = 3 (c + 7)$

Simplify $3 (c + 7)$ .

Apply the distributive property.

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

Multiply $3$ by $7$ .

$10 c = 3 c + 21$

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

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

$10 c - 3 c = 21$

Subtract $3 c$ from $10 c$ .

$7 c = 21$

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

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

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

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

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

Divide $c$ by $1$ .

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

Simplify the right side.

Divide $21$ by $7$ .

$c = 3$