Precalculus Examples

$\log ({(4 x)}^{2})$

Step 1

Expand $\log ({(4 x)}^{2})$ by moving $2$ outside the logarithm.

$2 \log (4 x)$

Step 2

Rewrite $\log (4 x)$ as $\log (4) + \log (x)$ .

$2 (\log (4) + \log (x))$

Step 3

Simplify each term.

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Step 3.1

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

$2 (\log (2^{2}) + \log (x))$

Step 3.2

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

$2 (2 \log (2) + \log (x))$

Step 4

Apply the distributive property.

$2 (2 \log (2)) + 2 \log (x)$

Step 5

Multiply $2$ by $2$ .

$4 \log (2) + 2 \log (x)$