Trigonometry Examples

$\log_{5} (\frac{81}{x^{8}})$

Step 1

Rewrite $\log_{5} (\frac{81}{x^{8}})$ as $\log_{5} (81) - \log_{5} (x^{8})$ .

$\log_{5} (81) - \log_{5} (x^{8})$

Step 2

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

$\log_{5} (81) - (8 \log_{5} (x))$

Step 3

Multiply $8$ by $- 1$ .

$\log_{5} (81) - 8 \log_{5} (x)$

Step 4

Simplify each term.

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Step 4.1

Rewrite $\log_{5} (81)$ as $\log_{5} (3^{4})$ .

$\log_{5} (3^{4}) - 8 \log_{5} (x)$

Step 4.2

Expand $\log_{5} (3^{4})$ by moving $4$ outside the logarithm.

$4 \log_{5} (3) - 8 \log_{5} (x)$