Precalculus Examples

$\ln (36 d)$

Step 1

Rewrite $\ln (36 d)$ as $\ln (36) + \ln (d)$ .

$\ln (36) + \ln (d)$

Step 2

Simplify each term.

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Step 2.1

Rewrite $\ln (36)$ as $\ln (2^{2} \cdot 3^{2})$ .

$\ln (2^{2} \cdot 3^{2}) + \ln (d)$

Step 2.2

Rewrite $\ln (2^{2} \cdot 3^{2})$ as $\ln (2^{2}) + \ln (3^{2})$ .

$\ln (2^{2}) + \ln (3^{2}) + \ln (d)$

Step 2.3

Simplify each term.

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Step 2.3.1

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

$2 \ln (2) + \ln (3^{2}) + \ln (d)$

Step 2.3.2

Expand $\ln (3^{2})$ by moving $2$ outside the logarithm.

$2 \ln (2) + 2 \ln (3) + \ln (d)$