Results 1 to 5 of 5

Math Help - Amount of numbers in an exponent

  1. #1
    Newbie
    Joined
    Nov 2011
    From
    Bruxelles
    Posts
    5

    Amount of numbers in an exponent

    sorry for my english and sorry if it's not the right forum

    i'm asked to say the amount of numbers of 2^56, and I don't know how!
    thank u!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,277
    Thanks
    669

    Re: Amount of numbers in an exponent

    do you mean the number of digits?

    if so we want to find an integer x so that 10^(x) < 2^56 < 10^(x+1).

    taking common logarithms: x < log(2^56) < x+1

    x < 56(log(2)) < x+1

    log(2) is approx. 0.301, so 56(0.301) = 16.856....therefore 2^56 has 17 digits.

    (10^x has x+1 digits, a 1 and x 0's after)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2011
    From
    Bruxelles
    Posts
    5

    Re: Amount of numbers in an exponent

    thank you, yes I meant it!

    but i still don't get why 2^56 has to be included between 10^x and 10^(x+1)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,277
    Thanks
    669

    Re: Amount of numbers in an exponent

    10^x is the smallest number with x+1 digits, and 10^(x+1) is the smallest number with x+2 digits.

    for example: 10 is the smallest number with 2 digits (9 has just one digit), and 100 is the smallest number with 3 digits (99 has only 2).

    so if a number has 2 digits, it lies between 10 and 100.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2011
    From
    Bruxelles
    Posts
    5

    Re: Amount of numbers in an exponent

    thank you for the clear explanation!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: April 27th 2011, 04:53 PM
  2. Finding amount of numbers.
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 10th 2010, 12:28 AM
  3. [SOLVED] Help dividing exponent by exponent
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 29th 2010, 11:20 AM
  4. Inclusion/exclusion principle for amount of numbers
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: November 10th 2009, 04:47 PM
  5. Replies: 1
    Last Post: August 19th 2008, 08:41 AM

Search Tags


/mathhelpforum @mathhelpforum