Precalculus Examples

$\ln (\frac{(1 - p) d}{\sqrt[6]{2 + 5 r}})$

Step 1

Rewrite $\ln (\frac{(1 - p) d}{\sqrt[6]{2 + 5 r}})$ as $\ln ((1 - p) d) - \ln (\sqrt[6]{2 + 5 r})$ .

$\ln ((1 - p) d) - \ln (\sqrt[6]{2 + 5 r})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[6]{2 + 5 r}$ as ${(2 + 5 r)}^{\frac{1}{6}}$ .

$\ln ((1 - p) d) - \ln ({(2 + 5 r)}^{\frac{1}{6}})$

Step 3

Expand $\ln ({(2 + 5 r)}^{\frac{1}{6}})$ by moving $\frac{1}{6}$ outside the logarithm.

$\ln ((1 - p) d) - (\frac{1}{6} \ln (2 + 5 r))$

Step 4

Combine $\frac{1}{6}$ and $\ln (2 + 5 r)$ .

$\ln ((1 - p) d) - \frac{\ln (2 + 5 r)}{6}$

Step 5

Rewrite $\ln ((1 - p) d)$ as $\ln (1 - p) + \ln (d)$ .

$\ln (1 - p) + \ln (d) - \frac{\ln (2 + 5 r)}{6}$

Step 6

To write $\ln (1 - p)$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\ln (1 - p) \cdot \frac{6}{6} - \frac{\ln (2 + 5 r)}{6} + \ln (d)$

Step 7

Combine $\ln (1 - p)$ and $\frac{6}{6}$ .

$\frac{\ln (1 - p) \cdot 6}{6} - \frac{\ln (2 + 5 r)}{6} + \ln (d)$

Step 8

Combine the numerators over the common denominator.

$\frac{\ln (1 - p) \cdot 6 - \ln (2 + 5 r)}{6} + \ln (d)$

Step 9

Move $6$ to the left of $\ln (1 - p)$ .

$\frac{6 \ln (1 - p) - \ln (2 + 5 r)}{6} + \ln (d)$