Precalculus Examples

$\log_{2} (x) + \log_{2} (x - 3)$

Step 1

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

$\log_{2} (x (x - 3))$

Step 2

Apply the distributive property.

$\log_{2} (x \cdot x + x \cdot - 3)$

Step 3

Simplify the expression.

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Step 3.1

Multiply $x$ by $x$ .

$\log_{2} (x^{2} + x \cdot - 3)$

Step 3.2

Move $- 3$ to the left of $x$ .

$\log_{2} (x^{2} - 3 x)$