Precalculus Examples

$\log_{8} ({(\frac{x^{2} - 9}{{(x + 2)}^{2}})}^{3})$

Step 1

Expand $\log_{8} ({(\frac{x^{2} - 9}{{(x + 2)}^{2}})}^{3})$ by moving $3$ outside the logarithm.

$3 \log_{8} (\frac{x^{2} - 9}{{(x + 2)}^{2}})$

Step 2

Rewrite $\log_{8} (\frac{x^{2} - 9}{{(x + 2)}^{2}})$ as $\log_{8} (x^{2} - 9) - \log_{8} ({(x + 2)}^{2})$ .

$3 (\log_{8} (x^{2} - 9) - \log_{8} ({(x + 2)}^{2}))$

Step 3

Expand $\log_{8} ({(x + 2)}^{2})$ by moving $2$ outside the logarithm.

$3 (\log_{8} (x^{2} - 9) - (2 \log_{8} (x + 2)))$

Step 4

Multiply $2$ by $- 1$ .

$3 (\log_{8} (x^{2} - 9) - 2 \log_{8} (x + 2))$

Step 5

Apply the distributive property.

$3 \log_{8} (x^{2} - 9) + 3 (- 2 \log_{8} (x + 2))$

Step 6

Multiply $- 2$ by $3$ .

$3 \log_{8} (x^{2} - 9) - 6 \log_{8} (x + 2)$