# How do you calculate log_2 (3.16)?

May 5, 2016

${\log}_{2} \left(3.16\right) = \log \frac{3.16}{\log} \left(2\right) \approx 1.66$

#### Explanation:

Using the change of base formula, we have:

${\log}_{2} \left(3.16\right) = \log \frac{3.16}{\log} \left(2\right)$

One way of finding an approximation for this is to note that:

$\sqrt{10} \approx 3.16227766 \approx 3.16$

So:

$\log \left(3.16\right) \approx \log \left({10}^{\frac{1}{2}}\right) = \frac{1}{2}$

Also use:

$\log \left(2\right) \approx 0.30103$

Then:

${\log}_{2} \left(3.16\right) = \log \frac{3.16}{\log} \left(2\right) \approx \frac{1}{2 \cdot 0.30103} = \frac{1}{0.60206} \approx 1.66$