Question

How do you calculate `log_7 5.8` with a calculator?

Answer 1

`log_7 5.8 = (log_10 5.8)/(log_10 7) = 0.9034`

Explanation:

Some calculators are able to calculate logs with any base, but let's work through this for those calculators which can only work with base 10.

Let `log_7 5.8 = x" log form"`

`7^x = 5.8" index form"`

The variable is in the index, find the log of both sides.

`log_10 7^x = log_10 5.8`

`xlog_10 7 = log_10 5.8`

`x = (log_10 5.8)/(log_10 7)`

Now use a calculator to find the answer `0.9034`

`log_a b = (log_10 b)/(log_10 a) " is called the change of base law"`

We could have written the following in one step:

`log_7 5.8 = (log_10 5.8)/(log_10 7)`