Precalculus Examples

$\log_{2} (10 x)$

Step 1

Rewrite $\log_{2} (10 x)$ as $\log_{2} (10) + \log_{2} (x)$ .

$\log_{2} (10) + \log_{2} (x)$

Step 2

Simplify each term.

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Step 2.1

Rewrite $\log_{2} (10)$ as $\log_{2} (2 (5))$ .

$\log_{2} (2 (5)) + \log_{2} (x)$

Step 2.2

Rewrite $\log_{2} (2 (5))$ as $\log_{2} (2) + \log_{2} (5)$ .

$\log_{2} (2) + \log_{2} (5) + \log_{2} (x)$

Step 2.3

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

$1 + \log_{2} (5) + \log_{2} (x)$