Solve for y 9^(3y)=27^(y-4)

$9^{3 y} = 27^{y - 4}$

Step 1

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

$3^{2 (3 y)} = 3^{3 (y - 4)}$

Step 2

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

$2 (3 y) = 3 (y - 4)$

Step 3

Solve for $y$ .

Multiply $3$ by $2$ .

$6 y = 3 (y - 4)$

Simplify $3 (y - 4)$ .

Apply the distributive property.

$6 y = 3 y + 3 \cdot - 4$

Multiply $3$ by $- 4$ .

$6 y = 3 y - 12$

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

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

$6 y - 3 y = - 12$

Subtract $3 y$ from $6 y$ .

$3 y = - 12$

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

Divide each term in $3 y = - 12$ by $3$ .

$\frac{3 y}{3} = \frac{- 12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 12}{3}$

Divide $y$ by $1$ .

$y = \frac{- 12}{3}$

Simplify the right side.

Divide $- 12$ by $3$ .

$y = - 4$