Precalculus Examples

$2 \log_{3} (x + 3) - \log_{3} (x - 15) - \log_{3} (x - 6)$

Step 1

Simplify $2 \log_{3} (x + 3)$ by moving $2$ inside the logarithm.

$\log_{3} ({(x + 3)}^{2}) - \log_{3} (x - 15) - \log_{3} (x - 6)$

Step 2

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

$\log_{3} (\frac{{(x + 3)}^{2}}{x - 15}) - \log_{3} (x - 6)$

Step 3

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

$\log_{3} (\frac{\frac{{(x + 3)}^{2}}{x - 15}}{x - 6})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\log_{3} (\frac{{(x + 3)}^{2}}{x - 15} \cdot \frac{1}{x - 6})$

Step 5

Multiply $\frac{{(x + 3)}^{2}}{x - 15}$ by $\frac{1}{x - 6}$ .

$\log_{3} (\frac{{(x + 3)}^{2}}{(x - 15) (x - 6)})$