Results 1 to 5 of 5

Math Help - Exponential equation

  1. #1
    Newbie
    Joined
    Oct 2010
    Posts
    2

    Exponential equation

    Hi guys

    I can't solve the following exponential equation:

    n * 11^n = 132

    Any help will be appreciated!

    Thanks in advance,

    Matan
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by matancs92 View Post
    Hi guys

    I can't solve the following exponential equation:

    n * 11^n = 132

    Any help will be appreciated!

    Thanks in advance,

    Matan
    you'll need to use technology (a calculator or computer) to solve this equation ... n \approx 1.7928...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member Educated's Avatar
    Joined
    Aug 2010
    From
    New Zealand
    Posts
    421
    Thanks
    11
    n11^n = 132

    You cannot solve this normally, or get the exact result of it. You can only get an approximation of it (down to however many decimal places you want.)

    A method that can be used to solve this is the Newton–Raphson method. x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}

    Rearrange the formula to make one side equal zero, n11^n -132= 0 and call this f(x).
    Select an appropriate number to start off with, call this x_0 and apply the newton method.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,368
    Thanks
    1313
    You can give an "algebraic" solution in terms of the Lambert W function, W(x), which is defined as the inverse function to f(x)= xe^x.

    Of course, 11^n= e^{ln(11^n)}= e^{n ln(11)}. If we let y= n ln(11), then n= \frac{y}{ln(11)} and the equation becomes \frac{ye^y}{ln(11)}= 132.

    Then ye^y= 132ln(11) so y= n ln(11)=  W(132 ln(11)) and n= \frac{W(132 ln(11))}{ln(11)}.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2010
    Posts
    2
    Thank you very much for helping me guys!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. exponential equation
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: February 6th 2010, 10:46 AM
  2. Exponential Equation help!
    Posted in the Algebra Forum
    Replies: 3
    Last Post: November 19th 2009, 02:36 PM
  3. exponential equation
    Posted in the Algebra Forum
    Replies: 2
    Last Post: November 5th 2008, 12:13 AM
  4. Please help with this exponential equation
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 21st 2007, 11:27 PM
  5. Exponential equation
    Posted in the Algebra Forum
    Replies: 2
    Last Post: July 22nd 2007, 09:33 AM

Search Tags


/mathhelpforum @mathhelpforum