Precalculus Examples

$\ln ({(4 x)}^{2}) + \ln (4) - 2$

Step 1

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

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

Step 2

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

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

Step 3

Simplify each term.

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Step 3.1

Simplify each term.

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Step 3.1.1

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

$2 (\ln (2^{2}) + \ln (x)) + \ln (4) - 2$

Step 3.1.2

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

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

Step 3.2

Apply the distributive property.

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

Step 3.3

Multiply $2$ by $2$ .

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

Step 3.4

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

$4 \ln (2) + 2 \ln (x) + \ln (2^{2}) - 2$

Step 3.5

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

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

Step 4

Add $4 \ln (2)$ and $2 \ln (2)$ .

$6 \ln (2) + 2 \ln (x) - 2$