log4 1/16?

Question

what is the easiest way to evaluate this?

Answer 1

log4 [16^(-1) ]
= (-1) log4 16
= (-1) (2)
= - 2

Answer 2

log4 1/16 =log4 4^-2= -2

Answer 3

log[n] (X) = ln(X) / ln(n)

log[4](1/16) = ln(1/16)/ln(4) = -2


Another way of thinking of it is:

4 to some X power = 1/16

you can see that X has to be negative to create
a fraction, and the since 16 is 4 squared, you can
see that the magnitude of the exponent is 2.

So log[4] (1/16) = -2 [ie. 4^(-2) = 1/16]