Trigonometry Examples

$\log_{a} (\frac{x^{7}}{y z^{8}})$

Step 1

Rewrite $\log_{a} (\frac{x^{7}}{y z^{8}})$ as $\log_{a} (x^{7}) - \log_{a} (y z^{8})$ .

$\log_{a} (x^{7}) - \log_{a} (y z^{8})$

Step 2

Expand $\log_{a} (x^{7})$ by moving $7$ outside the logarithm.

$7 \log_{a} (x) - \log_{a} (y z^{8})$

Step 3

Rewrite $\log_{a} (y z^{8})$ as $\log_{a} (y) + \log_{a} (z^{8})$ .

$7 \log_{a} (x) - (\log_{a} (y) + \log_{a} (z^{8}))$

Step 4

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

$7 \log_{a} (x) - (\log_{a} (y) + 8 \log_{a} (z))$

Step 5

Simplify each term.

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Step 5.1

Apply the distributive property.

$7 \log_{a} (x) - \log_{a} (y) - (8 \log_{a} (z))$

Step 5.2

Multiply $8$ by $- 1$ .

$7 \log_{a} (x) - \log_{a} (y) - 8 \log_{a} (z)$