Precalculus Examples

$\log (\sqrt[9]{\frac{5}{t}})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[9]{\frac{5}{t}}$ as ${(\frac{5}{t})}^{\frac{1}{9}}$ .

$\log ({(\frac{5}{t})}^{\frac{1}{9}})$

Expand $\log ({(\frac{5}{t})}^{\frac{1}{9}})$ by moving $\frac{1}{9}$ outside the logarithm.

$\frac{1}{9} \log (\frac{5}{t})$

Rewrite $\log (\frac{5}{t})$ as $\log (5) - \log (t)$ .

$\frac{1}{9} (\log (5) - \log (t))$

Apply the distributive property.

$\frac{1}{9} \log (5) + \frac{1}{9} (- \log (t))$

Combine $\frac{1}{9}$ and $\log (5)$ .

$\frac{\log (5)}{9} + \frac{1}{9} (- \log (t))$

Combine $\frac{1}{9}$ and $\log (t)$ .

$\frac{\log (5)}{9} - \frac{\log (t)}{9}$