Precalculus Examples

$2 \log_{3} (x + 9) - \log_{3} (x - 10) - \log_{3} (x - 13)$

Step 1

Simplify $2 \log_{3} (x + 9)$ by moving $2$ inside the logarithm.

$\log_{3} ({(x + 9)}^{2}) - \log_{3} (x - 10) - \log_{3} (x - 13)$

Step 2

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

$\log_{3} (\frac{{(x + 9)}^{2}}{x - 10}) - \log_{3} (x - 13)$

Step 3

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

$\log_{3} (\frac{\frac{{(x + 9)}^{2}}{x - 10}}{x - 13})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\log_{3} (\frac{{(x + 9)}^{2}}{x - 10} \cdot \frac{1}{x - 13})$

Step 5

Multiply $\frac{{(x + 9)}^{2}}{x - 10}$ by $\frac{1}{x - 13}$ .

$\log_{3} (\frac{{(x + 9)}^{2}}{(x - 10) (x - 13)})$