Expand the Logarithmic Expression log base 3 of ((3x)/y)^2

$\log_{3} ({(\frac{3 x}{y})}^{2})$

Expand $\log_{3} ({(\frac{3 x}{y})}^{2})$ by moving $2$ outside the logarithm.

$2 \log_{3} (\frac{3 x}{y})$

Rewrite $\log_{3} (\frac{3 x}{y})$ as $\log_{3} (3 x) - \log_{3} (y)$ .

$2 (\log_{3} (3 x) - \log_{3} (y))$

Rewrite $\log_{3} (3 x)$ as $\log_{3} (3) + \log_{3} (x)$ .

$2 (\log_{3} (3) + \log_{3} (x) - \log_{3} (y))$

Logarithm base $3$ of $3$ is $1$ .

$2 (1 + \log_{3} (x) - \log_{3} (y))$

Apply the distributive property.

$2 \cdot 1 + 2 \log_{3} (x) + 2 (- \log_{3} (y))$

Simplify.

Multiply $2$ by $1$ .

$2 + 2 \log_{3} (x) + 2 (- \log_{3} (y))$

Multiply $- 1$ by $2$ .

$2 + 2 \log_{3} (x) - 2 \log_{3} (y)$