Precalculus Examples

$\log_{14} (x^{2} - 1) - \log_{14} (x + 1)$

Step 1

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

$\log_{14} (\frac{x^{2} - 1}{x + 1})$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Rewrite $1$ as $1^{2}$ .

$\log_{14} (\frac{x^{2} - 1^{2}}{x + 1})$

Step 2.2

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 $b = 1$ .

$\log_{14} (\frac{(x + 1) (x - 1)}{x + 1})$

Step 3

Cancel the common factor of $x + 1$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

$\log_{14} (\frac{(x + 1) (x - 1)}{x + 1})$

Step 3.2

Divide $x - 1$ by $1$ .

$\log_{14} (x - 1)$