Precalculus Examples

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

Step 1

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

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

Step 2

Simplify each term.

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Step 2.1

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

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

Step 2.2

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

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

Step 3

Apply the distributive property.

$2 \log (2 x - (2 \log (2)) - \log (x))$

Step 4

Multiply $2$ by $- 1$ .

$2 \log (2 x - 2 \log (2) - \log (x))$