Precalculus Examples

$\log_{6} (\frac{\sqrt{f}}{36})$

Step 1

Rewrite $\log_{6} (\frac{\sqrt{f}}{36})$ as $\log_{6} (\sqrt{f}) - \log_{6} (36)$ .

$\log_{6} (\sqrt{f}) - \log_{6} (36)$

Step 2

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

$\log_{6} (f^{\frac{1}{2}}) - \log_{6} (36)$

Step 3

Expand $\log_{6} (f^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log_{6} (f) - \log_{6} (36)$

Step 4

Logarithm base $6$ of $36$ is $2$ .

$\frac{1}{2} \log_{6} (f) - 1 \cdot 2$

Step 5

Multiply $- 1$ by $2$ .

$\frac{1}{2} \log_{6} (f) - 2$

Step 6

Combine $\frac{1}{2}$ and $\log_{6} (f)$ .

$\frac{\log_{6} (f)}{2} - 2$