Precalculus Examples

$\log (x \sqrt{y^{5}})$

Step 1

Rewrite $\log (x \sqrt{y^{5}})$ as $\log (x) + \log (\sqrt{y^{5}})$ .

$\log (x) + \log (\sqrt{y^{5}})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y^{5}}$ as $y^{\frac{5}{2}}$ .

$\log (x) + \log (y^{\frac{5}{2}})$

Step 3

Expand $\log (y^{\frac{5}{2}})$ by moving $\frac{5}{2}$ outside the logarithm.

$\log (x) + \frac{5}{2} \log (y)$

Step 4

Combine $\frac{5}{2}$ and $\log (y)$ .

$\log (x) + \frac{5 \log (y)}{2}$