Precalculus Examples

$4 \log_{3} (x + 8) - \log_{3} (x - 12) - \log_{3} (x - 20)$

Step 1

Simplify $4 \log_{3} (x + 8)$ by moving $4$ inside the logarithm.

$\log_{3} ({(x + 8)}^{4}) - \log_{3} (x - 12) - \log_{3} (x - 20)$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{3} (\frac{{(x + 8)}^{4}}{x - 12}) - \log_{3} (x - 20)$

Step 3

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{3} (\frac{\frac{{(x + 8)}^{4}}{x - 12}}{x - 20})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\log_{3} (\frac{{(x + 8)}^{4}}{x - 12} \cdot \frac{1}{x - 20})$

Step 5

Multiply $\frac{{(x + 8)}^{4}}{x - 12}$ by $\frac{1}{x - 20}$ .

$\log_{3} (\frac{{(x + 8)}^{4}}{(x - 12) (x - 20)})$