Solve for b 36^(3b)=216^(b+4)

$36^{3 b} = 216^{b + 4}$

Step 1

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

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

Step 2

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

$2 (3 b) = 3 (b + 4)$

Step 3

Solve for $b$ .

Multiply $3$ by $2$ .

$6 b = 3 (b + 4)$

Simplify $3 (b + 4)$ .

Apply the distributive property.

$6 b = 3 b + 3 \cdot 4$

Multiply $3$ by $4$ .

$6 b = 3 b + 12$

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

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

$6 b - 3 b = 12$

Subtract $3 b$ from $6 b$ .

$3 b = 12$

Divide each term in $3 b = 12$ by $3$ and simplify.

Divide each term in $3 b = 12$ by $3$ .

$\frac{3 b}{3} = \frac{12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 b}{3} = \frac{12}{3}$

Divide $b$ by $1$ .

$b = \frac{12}{3}$

Simplify the right side.

Divide $12$ by $3$ .

$b = 4$