Question

If the function f is defined by f(x) = In(logx), what is f(0.1)?

Answer 1

f(0.1) =
`i \pi`

Explanation:

Plug x = 0.1.

Therefore f(0.1) = ln (log (0.1)).

0.1 = 10^(-1), and by the definition of log, log 0.1 = -1.

Now f(0.1) = ln (-1).

By Euler's identity, e^(i pi) = -1.

So ln (-1) would be i pi.

f(0.1) =
`i \pi`