Precalculus Examples

$\ln (10 \sqrt{m})$

Rewrite $\ln (10 \sqrt{m})$ as $\ln (10) + \ln (\sqrt{m})$ .

$\ln (10) + \ln (\sqrt{m})$

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

$\ln (10) + \ln (m^{\frac{1}{2}})$

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

$\ln (10) + \frac{1}{2} \ln (m)$

Simplify each term.

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

$\ln (2 (5)) + \frac{1}{2} \ln (m)$

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

$\ln (2) + \ln (5) + \frac{1}{2} \ln (m)$

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

$\ln (2) + \ln (5) + \frac{\ln (m)}{2}$