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

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Answer 1 · 2016-08-12T21:29:07

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

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 $k$ .

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