Simplify/Condense log of x+6+ log of x-6

$\log (x + 6) + \log (x - 6)$

Step 1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log ((x + 6) (x - 6))$

Step 2

Expand $(x + 6) (x - 6)$ using the FOIL Method.

Apply the distributive property.

$\log (x (x - 6) + 6 (x - 6))$

Apply the distributive property.

$\log (x \cdot x + x \cdot - 6 + 6 (x - 6))$

Apply the distributive property.

$\log (x \cdot x + x \cdot - 6 + 6 x + 6 \cdot - 6)$

Step 3

Simplify terms.

Combine the opposite terms in $x \cdot x + x \cdot - 6 + 6 x + 6 \cdot - 6$ .

Reorder the factors in the terms $x \cdot - 6$ and $6 x$ .

$\log (x \cdot x - 6 x + 6 x + 6 \cdot - 6)$

Add $- 6 x$ and $6 x$ .

$\log (x \cdot x + 0 + 6 \cdot - 6)$

Add $x \cdot x$ and $0$ .

$\log (x \cdot x + 6 \cdot - 6)$

Simplify each term.

Multiply $x$ by $x$ .

$\log (x^{2} + 6 \cdot - 6)$

Multiply $6$ by $- 6$ .

$\log (x^{2} - 36)$