Expand the Logarithmic Expression ( log base 3 of 2)( log base 3 of 4)

$(\log_{3} (2)) (\log_{3} (4))$

Rewrite $\log_{3} (4)$ as $\log_{3} (2^{2})$ .

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

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

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

Multiply $\log_{3} (2) (2 \log_{3} (2))$ .

Raise $\log_{3} (2)$ to the power of $1$ .

$2 ({\log_{3}}^{1} (2) \log_{3} (2))$

Raise $\log_{3} (2)$ to the power of $1$ .

$2 ({\log_{3}}^{1} (2) {\log_{3}}^{1} (2))$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 {\log_{3} (2)}^{1 + 1}$

Add $1$ and $1$ .

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