Precalculus Examples

$2 \log_{6} (x + 6) - \log_{6} (x - 19) - \log_{6} (x - 2)$

Step 1

Simplify $2 \log_{6} (x + 6)$ by moving $2$ inside the logarithm.

$\log_{6} ({(x + 6)}^{2}) - \log_{6} (x - 19) - \log_{6} (x - 2)$

Step 2

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

$\log_{6} (\frac{{(x + 6)}^{2}}{x - 19}) - \log_{6} (x - 2)$

Step 3

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

$\log_{6} (\frac{\frac{{(x + 6)}^{2}}{x - 19}}{x - 2})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\log_{6} (\frac{{(x + 6)}^{2}}{x - 19} \cdot \frac{1}{x - 2})$

Step 5

Multiply $\frac{{(x + 6)}^{2}}{x - 19}$ by $\frac{1}{x - 2}$ .

$\log_{6} (\frac{{(x + 6)}^{2}}{(x - 19) (x - 2)})$