Algebra Examples

$\log_{6} ({(\frac{8}{5})}^{4})$

Step 1

Expand $\log_{6} ({(\frac{8}{5})}^{4})$ by moving $4$ outside the logarithm.

$4 \log_{6} (\frac{8}{5})$

Step 2

Rewrite $\log_{6} (\frac{8}{5})$ as $\log_{6} (8) - \log_{6} (5)$ .

$4 (\log_{6} (8) - \log_{6} (5))$

Step 3

Simplify each term.

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Step 3.1

Rewrite $\log_{6} (8)$ as $\log_{6} (2^{3})$ .

$4 (\log_{6} (2^{3}) - \log_{6} (5))$

Step 3.2

Expand $\log_{6} (2^{3})$ by moving $3$ outside the logarithm.

$4 (3 \log_{6} (2) - \log_{6} (5))$

Step 4

Apply the distributive property.

$4 (3 \log_{6} (2)) + 4 (- \log_{6} (5))$

Step 5

Multiply $3$ by $4$ .

$12 \log_{6} (2) + 4 (- \log_{6} (5))$

Step 6

Multiply $- 1$ by $4$ .

$12 \log_{6} (2) - 4 \log_{6} (5)$