Question

Special Sequence and Series

Find ln(–256.7).

Answer 1

`5.5479 + \pi i`

Explanation:

In the real domain,
`l n ( x )` is undefined for
`x < 0`.

And because most of the calculators run in the real domain only so they will show an error (E) for this.

`ln(-1) = \pi i`

We know that
`ln(a * b) = ln(a) + ln(b)`.

`ln(-265.7) = ln[256.7 * (-1)]`

`ln(256.7) + ln(-1) = ln(256.7) + \pi i = 5.5479 + \pi i`

Answer 2

ln(-256) = 5.54 + πi

Explanation:

We have to find ln(-256)

This question belongs to the complex domain which says

ln(-1)= πi

So ln(-256)= ln(256*(-1))

And we know that ln(a*b)= ln(a)+ln(b)

So, ln(256*(-1))= ln(256)+(ln-1)

as ln(-1)= πi, putting value and finding ln(256) we get,

ln(256*(-1)) = 5.54 + πi