Expand the Logarithmic Expression log base 9 of (x^6)/(4y)

$\log_{9} (\frac{x^{6}}{4 y})$

Rewrite $\log_{9} (\frac{x^{6}}{4 y})$ as $\log_{9} (x^{6}) - \log_{9} (4 y)$ .

$\log_{9} (x^{6}) - \log_{9} (4 y)$

Expand $\log_{9} (x^{6})$ by moving $6$ outside the logarithm.

$6 \log_{9} (x) - \log_{9} (4 y)$

Rewrite $\log_{9} (4 y)$ as $\log_{9} (4) + \log_{9} (y)$ .

$6 \log_{9} (x) - (\log_{9} (4) + \log_{9} (y))$

Simplify each term.

Rewrite $\log_{9} (4)$ as $\log_{9} (2^{2})$ .

$6 \log_{9} (x) - (\log_{9} (2^{2}) + \log_{9} (y))$

Expand $\log_{9} (2^{2})$ by moving $2$ outside the logarithm.

$6 \log_{9} (x) - (2 \log_{9} (2) + \log_{9} (y))$

Apply the distributive property.

$6 \log_{9} (x) - (2 \log_{9} (2)) - \log_{9} (y)$

Multiply $2$ by $- 1$ .

$6 \log_{9} (x) - 2 \log_{9} (2) - \log_{9} (y)$