Question

What is `log 50` to `3` decimal places?

Answer 1

`log 50 ~~ 1.699`

Explanation:

Note that `50 = 100/2`

So:

`log 50 = log (100/2) = log 100 - log 2 ~~ 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 ~~ 0.30103` we get:

`log 50 ~~ 2-0.30103 = 1.69897`