Precalculus Examples

$\ln (16 x^{4} {(4 x + 9)}^{2})$

Step 1

Rewrite $\ln (16 x^{4} {(4 x + 9)}^{2})$ as $\ln (16 x^{4}) + \ln ({(4 x + 9)}^{2})$ .

$\ln (16 x^{4}) + \ln ({(4 x + 9)}^{2})$

Step 2

Rewrite $\ln (16 x^{4})$ as $\ln (16) + \ln (x^{4})$ .

$\ln (16) + \ln (x^{4}) + \ln ({(4 x + 9)}^{2})$

Step 3

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

$\ln (16) + 4 \ln (x) + \ln ({(4 x + 9)}^{2})$

Step 4

Expand $\ln ({(4 x + 9)}^{2})$ by moving $2$ outside the logarithm.

$\ln (16) + 4 \ln (x) + 2 \ln (4 x + 9)$

Step 5

Simplify each term.

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Step 5.1

Rewrite $\ln (16)$ as $\ln (2^{4})$ .

$\ln (2^{4}) + 4 \ln (x) + 2 \ln (4 x + 9)$

Step 5.2

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

$4 \ln (2) + 4 \ln (x) + 2 \ln (4 x + 9)$