Precalculus Examples

$\log_{4} ({(\frac{x^{2} - 9}{x^{2} - 6 x + 8})}^{\frac{1}{3}})$

Step 1

Expand $\log_{4} ({(\frac{x^{2} - 9}{x^{2} - 6 x + 8})}^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$\frac{1}{3} \log_{4} (\frac{x^{2} - 9}{x^{2} - 6 x + 8})$

Step 2

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

$\frac{1}{3} (\log_{4} (x^{2} - 9) - \log_{4} (x^{2} - 6 x + 8))$

Step 3

Apply the distributive property.

$\frac{1}{3} \log_{4} (x^{2} - 9) + \frac{1}{3} (- \log_{4} (x^{2} - 6 x + 8))$

Step 4

Combine $\frac{1}{3}$ and $\log_{4} (x^{2} - 9)$ .

$\frac{\log_{4} (x^{2} - 9)}{3} + \frac{1}{3} (- \log_{4} (x^{2} - 6 x + 8))$

Step 5

Combine $\frac{1}{3}$ and $\log_{4} (x^{2} - 6 x + 8)$ .

$\frac{\log_{4} (x^{2} - 9)}{3} - \frac{\log_{4} (x^{2} - 6 x + 8)}{3}$

Step 6

Combine the numerators over the common denominator.

$\frac{\log_{4} (x^{2} - 9) - \log_{4} (x^{2} - 6 x + 8)}{3}$