Question

How do you calculate `log_5 33` with a calculator?

Answer 1

`log_5 33=2.1724`

Explanation:

The easiest way to solve such problems is to first change it to base `10`, as tables for base `10` are easily available. For this we can use the identity `log_b a=loga/logb`, where `loga` and `logb` are to base `10` (if base is not mentioned, it is taken as `10` and if base is `e`, we use `ln` - for natural logarithm).

Here, we have `log_5 33` and it is equal to `log33/log5` and from tables this is equal to

`1.5185/0.6990`

= `2.1724`

For using scientific calculator just press `5` and then button `log`, which gives `0.6990` (up to four places of decimals), now put this number in memory. Now press `33` and then button `log`, which gives `1.5185` up to four places of decimals. Now divide by memory recall (which has `0.6990` in memory) to get answer.