# How do you simplify 10^(log sqrt x )?

Aug 30, 2016

$\sqrt{x}$
(Assuming $\log = {\log}_{10}$)

#### Explanation:

Consider:$a = {10}^{b} \to {\log}_{10} a = b$

In this example: $y = {10}^{{\log}_{10} \sqrt{x}}$

So, $a = y$ and $b = {\log}_{10} \sqrt{x}$ in this case

$\therefore {\log}_{10} y = {\log}_{10} \sqrt{x}$

Hence $y = \sqrt{x}$