Precalculus Examples

$\log_{7} (\frac{11 \sqrt{r}}{s})$

Step 1

Rewrite $\log_{7} (\frac{11 \sqrt{r}}{s})$ as $\log_{7} (11 \sqrt{r}) - \log_{7} (s)$ .

$\log_{7} (11 \sqrt{r}) - \log_{7} (s)$

Step 2

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

$\log_{7} (11 r^{\frac{1}{2}}) - \log_{7} (s)$

Step 3

Rewrite $\log_{7} (11 r^{\frac{1}{2}})$ as $\log_{7} (11) + \log_{7} (r^{\frac{1}{2}})$ .

$\log_{7} (11) + \log_{7} (r^{\frac{1}{2}}) - \log_{7} (s)$

Step 4

Expand $\log_{7} (r^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\log_{7} (11) + \frac{1}{2} \log_{7} (r) - \log_{7} (s)$

Step 5

Combine $\frac{1}{2}$ and $\log_{7} (r)$ .

$\log_{7} (11) + \frac{\log_{7} (r)}{2} - \log_{7} (s)$