Precalculus Examples

$\log (x - 1) + \log (x + 1)$

Step 1

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

$\log ((x - 1) (x + 1))$

Step 2

Expand $(x - 1) (x + 1)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$\log (x (x + 1) - 1 (x + 1))$

Step 2.2

Apply the distributive property.

$\log (x \cdot x + x \cdot 1 - 1 (x + 1))$

Step 2.3

Apply the distributive property.

$\log (x \cdot x + x \cdot 1 - 1 x - 1 \cdot 1)$

Step 3

Simplify terms.

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Step 3.1

Combine the opposite terms in $x \cdot x + x \cdot 1 - 1 x - 1 \cdot 1$ .

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Step 3.1.1

Reorder the factors in the terms $x \cdot 1$ and $- 1 x$ .

$\log (x \cdot x + 1 x - 1 x - 1 \cdot 1)$

Step 3.1.2

Subtract $1 x$ from $1 x$ .

$\log (x \cdot x + 0 - 1 \cdot 1)$

Step 3.1.3

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

$\log (x \cdot x - 1 \cdot 1)$

Step 3.2

Simplify each term.

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Step 3.2.1

Multiply $x$ by $x$ .

$\log (x^{2} - 1 \cdot 1)$

Step 3.2.2

Multiply $- 1$ by $1$ .

$\log (x^{2} - 1)$