Write as a Single Logarithm log of x^2-9- log of x+3

$\log (x^{2} - 9) - \log (x + 3)$

Step 1

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

$\log (\frac{x^{2} - 9}{x + 3})$

Step 2

Simplify the numerator.

Rewrite $9$ as $3^{2}$ .

$\log (\frac{x^{2} - 3^{2}}{x + 3})$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 3$ .

$\log (\frac{(x + 3) (x - 3)}{x + 3})$

Step 3

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\log (\frac{(x + 3) (x - 3)}{x + 3})$

Divide $x - 3$ by $1$ .

$\log (x - 3)$