Precalculus Examples

$\ln (A^{3} \cdot \sqrt{B})$

Step 1

Rewrite $\ln (A^{3} \cdot \sqrt{B})$ as $\ln (A^{3}) + \ln (\sqrt{B})$ .

$\ln (A^{3}) + \ln (\sqrt{B})$

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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