Expand the Logarithmic Expression log base 6 of ((x^5)/y)^6

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Trigonometry

$\log_{6} ({(\frac{x^{5}}{y})}^{6})$

Expand $\log_{6} ({(\frac{x^{5}}{y})}^{6})$ by moving $6$ outside the logarithm.

$6 \log_{6} (\frac{x^{5}}{y})$

Rewrite $\log_{6} (\frac{x^{5}}{y})$ as $\log_{6} (x^{5}) - \log_{6} (y)$ .

$6 (\log_{6} (x^{5}) - \log_{6} (y))$

Expand $\log_{6} (x^{5})$ by moving $5$ outside the logarithm.

$6 (5 \log_{6} (x) - \log_{6} (y))$

Apply the distributive property.

$6 (5 \log_{6} (x)) + 6 (- \log_{6} (y))$

Multiply $5$ by $6$ .

$30 \log_{6} (x) + 6 (- \log_{6} (y))$

Multiply $- 1$ by $6$ .

$30 \log_{6} (x) - 6 \log_{6} (y)$

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