Precalculus Examples

$\log_{7} (x - 4) + \log_{7} (x + 2) \cdot 1$

Step 1

Multiply $\log_{7} (x + 2)$ by $1$ .

$\log_{7} (x - 4) + \log_{7} (x + 2)$

Step 2

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

$\log_{7} ((x - 4) (x + 2))$

Step 3

Expand $(x - 4) (x + 2)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$\log_{7} (x (x + 2) - 4 (x + 2))$

Step 3.2

Apply the distributive property.

$\log_{7} (x \cdot x + x \cdot 2 - 4 (x + 2))$

Step 3.3

Apply the distributive property.

$\log_{7} (x \cdot x + x \cdot 2 - 4 x - 4 \cdot 2)$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $x$ by $x$ .

$\log_{7} (x^{2} + x \cdot 2 - 4 x - 4 \cdot 2)$

Step 4.1.2

Move $2$ to the left of $x$ .

$\log_{7} (x^{2} + 2 \cdot x - 4 x - 4 \cdot 2)$

Step 4.1.3

Multiply $- 4$ by $2$ .

$\log_{7} (x^{2} + 2 x - 4 x - 8)$

Step 4.2

Subtract $4 x$ from $2 x$ .

$\log_{7} (x^{2} - 2 x - 8)$