SOLUTION: log2log2log2log2log2(65536)

Question 1077743: log2log2log2log2log2(65536)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i think parentheses might make this more readable.

we'll also set it to y.

y = log2(log2(log2(log2(log2(65536)))))

you want to work from the inner set of parentheses out.

there are 5 sets of nested parentheses to remove.

log2(655536) = log(65536)/log(2) = 16

equation becomes y = log2(log2(log2(log2(16))))

log2(16) = log(16)/log(2) = 4

equation becomes y = log2(log2(log2(4)))

log2(4) = log(4)/log(2) = 2

equation becomes y = log2(log2(2))

log2(2) = log(2)/log(2) = 1

equation becomes y = log2(1)

log2(1) = log(1)/log(2) = 0

equation becomes y = 0

it's a recursive type function in that the output of the first pass becomes the input to the second pass and the output of the second pass becomes the input to the third pass, etc.

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