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

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

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

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

Rewrite $\log_{3} (2 x)$ as $\log_{3} (2) + \log_{3} (x)$ .

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

Apply the distributive property.

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