Calculus Examples

$\ln (4 \sqrt{3})$

Step 1

Rewrite $\ln (4 \sqrt{3})$ as $\ln (4) + \ln (\sqrt{3})$ .

$\ln (4) + \ln (\sqrt{3})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\ln (4) + \ln (3^{\frac{1}{2}})$

Step 3

Expand $\ln (3^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\ln (4) + \frac{1}{2} \ln (3)$

Step 4

Combine $\frac{1}{2}$ and $\ln (3)$ .

$\ln (4) + \frac{\ln (3)}{2}$

Step 5

Simplify each term.

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Step 5.1

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

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

Step 5.2

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

$2 \ln (2) + \frac{\ln (3)}{2}$