Question 280011
log of 1/16 in base 1/8 = x
what does x equal?

The change of base formula says:

1.) log base b (x) = (log base d (x))/(log base d (b))

Note that 1/8 = (1/2)^3 and that 1/16 = (1/2)^4.  Letting d = 1/2 in 1.) above we have:

x = log base 1/8 (1/16) = (log base 1/2 (1/16))/(log base 1/2 (1/8))
x = 4/3