# How do you evaluate sqrt(log2* 20-log16) ?

Nov 9, 2016

The expression can be evaluated to $2.19$.

#### Explanation:

$\implies \sqrt{20 \log 2 - \log 16}$

Use the rule $a \log n = \log {n}^{a}$.

$\implies \sqrt{\log \left({2}^{20}\right) - \log 16}$

$\implies \sqrt{\log 1 , 048 , 576 - \log 16}$

Now, use the rule $\log a - \log n = \log \left(\frac{a}{n}\right)$.

$\implies \sqrt{\log \left(65536\right)}$

This can be evaluated, but it cannot be simplified to exact form.

We have

$\implies 2.19$

Hopefully this helps!