Precalculus Examples

$\ln (20 \cdot 10)$

Step 1

Rewrite $\ln (20 \cdot 10)$ as $\ln (20) + \ln (10)$ .

$\ln (20) + \ln (10)$

Step 2

Simplify each term.

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Step 2.1

Rewrite $\ln (20)$ as $\ln (2^{2} \cdot 5)$ .

$\ln (2^{2} \cdot 5) + \ln (10)$

Step 2.2

Rewrite $\ln (2^{2} \cdot 5)$ as $\ln (2^{2}) + \ln (5)$ .

$\ln (2^{2}) + \ln (5) + \ln (10)$

Step 2.3

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

$2 \ln (2) + \ln (5) + \ln (10)$

Step 2.4

Rewrite $\ln (10)$ as $\ln (2 (5))$ .

$2 \ln (2) + \ln (5) + \ln (2 (5))$

Step 2.5

Rewrite $\ln (2 (5))$ as $\ln (2) + \ln (5)$ .

$2 \ln (2) + \ln (5) + \ln (2) + \ln (5)$

Step 3

Add $\ln (5)$ and $\ln (5)$ .

$2 \ln (2) + 2 \ln (5) + \ln (2)$

Step 4

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

$3 \ln (2) + 2 \ln (5)$