Question

How do you evaluate `log_.25 (-4)`?

Answer 1

The principal value of `log_(0.25)(-4)` is `-1-pi/(ln(4))i`

Explanation:

Use the change of base formula to find:

`log_(0.25)(-4) = ln(-4)/ln(0.25) = ln(-4)/(ln(1/4)) = ln(-4)/(-ln(4)) = (ln(4)+pi i)/(-ln(4))`

`= -1-pi/(ln(4)) i`

Note this is the principal value of the logarithm.

There are other solutions of `0.25^x = -4`, namely:

`x = -1-(pi(1+2k))/(ln(4))i`

for any integer `k`.