Precalculus Examples

$7^{\log_{7} (\sqrt{x})}$

Step 1

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

$7^{\log_{7} (x^{\frac{1}{2}})}$

Step 2

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

$7^{\frac{1}{2} \log_{7} (x)}$

Step 3

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

$7^{\frac{\log_{7} (x)}{2}}$