Precalculus Examples

$2 \log_{2} (6 x)$

Step 1

Rewrite $\log_{2} (6 x)$ as $\log_{2} (6) + \log_{2} (x)$ .

$2 (\log_{2} (6) + \log_{2} (x))$

Step 2

Simplify each term.

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Step 2.1

Rewrite $\log_{2} (6)$ as $\log_{2} (2 (3))$ .

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

Step 2.2

Rewrite $\log_{2} (2 (3))$ as $\log_{2} (2) + \log_{2} (3)$ .

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

Step 2.3

Logarithm base $2$ of $2$ is $1$ .

$2 (1 + \log_{2} (3) + \log_{2} (x))$

Step 3

Apply the distributive property.

$2 \cdot 1 + 2 \log_{2} (3) + 2 \log_{2} (x)$

Step 4

Multiply $2$ by $1$ .

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