Precalculus Examples

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

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$\log (5^{5^{\frac{1}{2}}})$

Step 2

Expand $\log (5^{5^{\frac{1}{2}}})$ by moving $5^{\frac{1}{2}}$ outside the logarithm.

$5^{\frac{1}{2}} \log (5)$