SOLUTION: If (N^17) = 2012 and the decimal representation of logN is 0.ABCDE... (where A, B, C, ... are digits), what is the value of the digit B?

Algebra ->  Exponents -> SOLUTION: If (N^17) = 2012 and the decimal representation of logN is 0.ABCDE... (where A, B, C, ... are digits), what is the value of the digit B?      Log On


   



Question 1186908: If (N^17) = 2012 and the decimal representation of logN is 0.ABCDE... (where A, B, C, ... are digits), what is the value of the digit B?
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

You are given

    N%5E17 = 2012.


Take logarithm base 10 of both sides.  You will get

    17*log(N) = log(2012).


Hence,

    log(N) = log%28%282012%29%29%2F17 = use your calculator and get = 0.1943...


The digit B is 9.    ANSWER

Solved.

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Quite simple and straightforward.