Expert: Steve Holleran - 9/10/2008

Question
Hi, how do you find the nth term in this logarithm sequence:
 log[base 2]8, log[base4]8, log[base8]8, log[base16]8, log[base32]8? Can you please show the steps? Thank you very much!!!

Answer
Hi Emily,

Try to compare the number that is changing to the term number:

   Term #       Term

      1          log[2] 8

      2          log[4] 8

      3          log[8] 8

      4          log[16] 8

      5          log[32] 8

Look at the base of the log each time:

 2 = 2^1

 4 = 2^2

 8 = 2^3

 16 = 2^4

 32 = 2^5    Notice how the power of two in the base is the same
             as the term #?

So, in general, you can say

            Term # n = log[2^n] 8


Hope this is okay.
Steve