Results 1 to 3 of 3

Math Help - Proving (URGENT)

  1. #1
    Newbie
    Joined
    Apr 2008
    Posts
    1

    Proving (URGENT)

    Help! Please!

    Prove that if n is an element of Z(the integers) and log2n is rational, then log2n is an integer.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jan 2008
    Posts
    588
    Thanks
    87
    Consider this:
    log_2 (n)^k = k log_2 (n)

    When n = 2, log_2 (2) = 1

    If n is not a power of 2, then
     log_2 n = \frac{ln (n)}{ln (2)}

    is ln 2 rational?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by vincentngtf View Post
    Help! Please!

    Prove that if n is an element of Z(the integers) and log2n is rational, then log2n is an integer.
    (We can assume that n>1).
    Suppose that \log_2 n = p/q where p/q is a positive rational number. This means 2^{p/q} = n\implies \left( 2^{p/q} \right)^q = n^q\implies 2^p = n^q. Now the fundamental theorem of arithmetic allows us to factorize n, the thing is that all factors much be 2's because the LHS is made out of two, thus, n=2^m. This means, 2^p = 2^{mq}. Thus, p=mq which means q|p which tells us that p/q is an integer.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. urgent help, proving something?
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: September 13th 2009, 11:36 AM
  2. Urgent Proving Identities
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: January 12th 2009, 02:59 AM
  3. PROVING IDENTITY..URGENT HELP
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: August 23rd 2008, 12:30 AM
  4. URGENT!! Proving Statemens about angles
    Posted in the Geometry Forum
    Replies: 2
    Last Post: December 16th 2007, 04:19 PM
  5. Replies: 1
    Last Post: December 27th 2006, 06:31 AM

Search Tags


/mathhelpforum @mathhelpforum