Precalculus Examples

$\log (\frac{v (x^{6} + 10)}{(x^{8} + 9) {(x^{2} - 4)}^{8}})$

Step 1

Rewrite $\log (\frac{v (x^{6} + 10)}{(x^{8} + 9) {(x^{2} - 4)}^{8}})$ as $\log (v (x^{6} + 10)) - \log ((x^{8} + 9) {(x^{2} - 4)}^{8})$ .

$\log (v (x^{6} + 10)) - \log ((x^{8} + 9) {(x^{2} - 4)}^{8})$

Step 2

Rewrite $\log ((x^{8} + 9) {(x^{2} - 4)}^{8})$ as $\log (x^{8} + 9) + \log ({(x^{2} - 4)}^{8})$ .

$\log (v (x^{6} + 10)) - (\log (x^{8} + 9) + \log ({(x^{2} - 4)}^{8}))$

Step 3

Expand $\log ({(x^{2} - 4)}^{8})$ by moving $8$ outside the logarithm.

$\log (v (x^{6} + 10)) - (\log (x^{8} + 9) + 8 \log (x^{2} - 4))$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$\log (v (x^{6} + 10)) - \log (x^{8} + 9) - (8 \log (x^{2} - 4))$

Step 4.2

Multiply $8$ by $- 1$ .

$\log (v (x^{6} + 10)) - \log (x^{8} + 9) - 8 \log (x^{2} - 4)$