Finite Math Examples

$\ln (\sqrt{\frac{P}{q^{2 r}}})$

Step 1

Rewrite $\sqrt{\frac{P}{q^{2 r}}}$ as $\frac{\sqrt{P}}{\sqrt{q^{2 r}}}$ .

$\ln (\frac{\sqrt{P}}{\sqrt{q^{2 r}}})$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $q^{2 r}$ as ${(q^{r})}^{2}$ .

$\ln (\frac{\sqrt{P}}{\sqrt{{(q^{r})}^{2}}})$

Step 2.2

Pull terms out from under the radical, assuming positive real numbers.

$\ln (\frac{\sqrt{P}}{q^{r}})$