# What is log 50 to 3 decimal places?

Apr 2, 2017

$\log 50 \approx 1.699$

#### Explanation:

Note that $50 = \frac{100}{2}$

So:

$\log 50 = \log \left(\frac{100}{2}\right) = \log 100 - \log 2 \approx 2 - 0.301 = 1.699$

Note that a very good approximation for $\log 2$ which is worth remembering is $0.30103$. The actual value of $\log 2$ is closer to $0.30102999566398$, so you actually get $8$ significant figure accuracy for the sake of remembering $5$ digits.

Using $\log 2 \approx 0.30103$ we get:

$\log 50 \approx 2 - 0.30103 = 1.69897$