Precalculus Examples

$2 \log_{6} (4 x)$

Step 1

Rewrite $\log_{6} (4 x)$ as $\log_{6} (4) + \log_{6} (x)$ .

$2 (\log_{6} (4) + \log_{6} (x))$

Step 2

Simplify each term.

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Step 2.1

Rewrite $\log_{6} (4)$ as $\log_{6} (2^{2})$ .

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

Step 2.2

Expand $\log_{6} (2^{2})$ by moving $2$ outside the logarithm.

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

Step 3

Apply the distributive property.

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

Step 4

Multiply $2$ by $2$ .

$4 \log_{6} (2) + 2 \log_{6} (x)$