Precalculus Examples

$\log ((s \sqrt{7}) t^{2})$

Step 1

Rewrite $\log ((s \sqrt{7}) t^{2})$ as $\log (s \sqrt{7}) + \log (t^{2})$ .

$\log (s \sqrt{7}) + \log (t^{2})$

Step 2

Rewrite $\log (s \sqrt{7})$ as $\log (s) + \log (\sqrt{7})$ .

$\log (s) + \log (\sqrt{7}) + \log (t^{2})$

Step 3

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$\log (s) + \log (7^{\frac{1}{2}}) + \log (t^{2})$

Step 4

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

$\log (s) + \frac{1}{2} \log (7) + \log (t^{2})$

Step 5

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

$\log (s) + \frac{1}{2} \log (7) + 2 \log (t)$

Step 6

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

$\log (s) + \frac{\log (7)}{2} + 2 \log (t)$