Solve for n log base 3 of 1/9=n/3

$\log_{3} (\frac{1}{9}) = \frac{n}{3}$

Step 1

Rewrite the equation as $\frac{n}{3} = \log_{3} (\frac{1}{9})$ .

$\frac{n}{3} = \log_{3} (\frac{1}{9})$

Step 2

Multiply both sides of the equation by $3$ .

$3 \frac{n}{3} = 3 \log_{3} (\frac{1}{9})$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{n}{3} = 3 \log_{3} (\frac{1}{9})$

Rewrite the expression.

$n = 3 \log_{3} (\frac{1}{9})$

Simplify the right side.

Simplify $3 \log_{3} (\frac{1}{9})$ .

Logarithm base $3$ of $\frac{1}{9}$ is $- 2$ .

$n = 3 \cdot - 2$

Multiply $3$ by $- 2$ .

$n = - 6$