Precalculus Examples

$\log (\frac{\sqrt{13}}{10})$

Step 1

Rewrite $\log (\frac{\sqrt{13}}{10})$ as $\log (\sqrt{13}) - \log (10)$ .

$\log (\sqrt{13}) - \log (10)$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{13}$ as $13^{\frac{1}{2}}$ .

$\log (13^{\frac{1}{2}}) - \log (10)$

Step 3

Expand $\log (13^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log (13) - \log (10)$

Step 4

Logarithm base $10$ of $10$ is $1$ .

$\frac{1}{2} \log (13) - 1 \cdot 1$

Step 5

Combine $\frac{1}{2}$ and $\log (13)$ .

$\frac{\log (13)}{2} - 1 \cdot 1$

Step 6

Multiply $- 1$ by $1$ .

$\frac{\log (13)}{2} - 1$