Precalculus Examples

$\log (\sqrt{a}) a^{2}$

Step 1

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

$\log (a^{\frac{1}{2}}) a^{2}$

Step 2

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

$\frac{1}{2} \log (a) a^{2}$

Step 3

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

$\frac{\log (a)}{2} a^{2}$

Step 4

Combine $\frac{\log (a)}{2}$ and $a^{2}$ .

$\frac{\log (a) a^{2}}{2}$

Step 5

Reorder factors in $\frac{\log (a) a^{2}}{2}$ .

$\frac{a^{2} \log (a)}{2}$