Results 1 to 2 of 2

Math Help - Logarithm problem

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    1

    Logarithm problem

    If log B base A = log A base B, then what is the value of (A)(B)? A and B are positive real numbers, neither A nor B is 1, and neither are equal.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by Russellboy View Post
    If log B base A = log A base B, then what is the value of (A)(B)? A and B are positive real numbers, neither A nor B is 1, and neither are equal.
    Use the base change formula:

    \log_b(a)=\dfrac{\ln(a)}{\ln(b)}

    Therefore:

    \log_b(a)=\log_a(b)~\implies~ \dfrac{\ln(a)}{\ln(b)} = \dfrac{\ln(b)}{\ln(a)}~ \implies~(\ln(a))^2=(\ln(b))^2

    (\ln(a))^2=(\ln(b))^2~\implies~(\ln(a))^2-(\ln(b))^2=0~\implies~ \left(\ln(a)-\ln(b)\right) \left(\ln(a)+\ln(b)\right)=0

    \ln(a)=\ln(b)~\implies~ a= b (this case is excluded!) or

    \ln(a)=-\ln(b)~\implies~ a= \dfrac1b

    Therefore:

    \boxed{a \cdot b = 1}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Logarithm problem
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: May 30th 2009, 04:18 AM
  2. help with this logarithm problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 6th 2008, 05:07 PM
  3. LOgarithm proBLeM
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: November 30th 2008, 04:50 AM
  4. logarithm problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: September 30th 2008, 05:02 PM
  5. Please help logarithm problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: April 1st 2006, 09:32 PM

Search Tags


/mathhelpforum @mathhelpforum