Simplify/Condense log of x+4+ log of x-4

$\log (x + 4) + \log (x - 4)$

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

$\log ((x + 4) (x - 4))$

Expand $(x + 4) (x - 4)$ using the FOIL Method.

Apply the distributive property.

$\log (x (x - 4) + 4 (x - 4))$

Apply the distributive property.

$\log (x \cdot x + x \cdot - 4 + 4 (x - 4))$

Apply the distributive property.

$\log (x \cdot x + x \cdot - 4 + 4 x + 4 \cdot - 4)$

Simplify terms.

Combine the opposite terms in $x \cdot x + x \cdot - 4 + 4 x + 4 \cdot - 4$ .

Reorder the factors in the terms $x \cdot - 4$ and $4 x$ .

$\log (x \cdot x - 4 x + 4 x + 4 \cdot - 4)$

Add $- 4 x$ and $4 x$ .

$\log (x \cdot x + 0 + 4 \cdot - 4)$

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

$\log (x \cdot x + 4 \cdot - 4)$

Simplify each term.

Multiply $x$ by $x$ .

$\log (x^{2} + 4 \cdot - 4)$

Multiply $4$ by $- 4$ .

$\log (x^{2} - 16)$