Results 1 to 3 of 3

Math Help - logarithmic equation

  1. #1
    Member
    Joined
    Apr 2013
    From
    Mahinog
    Posts
    91
    Thanks
    5

    logarithmic equation

    Show that alogcb =blogca
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,969
    Thanks
    1788
    Awards
    1

    Re: logarithmic equation

    Quote Originally Posted by Trefoil2727 View Post
    Show that alogcb =blogca
    \\\text{If }a^{\log_c(b)}=b^{\log_c(a)}\\\text{then }\log_c(b)}\log_c(a)}=\log_c(a)}\log_c(b)}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,454
    Thanks
    1868

    Re: logarithmic equation

    A true "direct proof" would go the other way.
    From the obviously true log_c(b)log_c(a)= log_c(a)log_c(b), by a "property of logarithms"
    log_c\left(b^{log_c(a)}\right)= log_c\left(a^{log_c(b)}\right)
    and then take c to the power of each side.

    Of course, Plato's proof is a perfectly good "synthetic proof" where you start with what you want to prove and manipulate it (here by taking the logarithm, base c, of both sides) to produce something that is "obviously true" and each step is reversible.
    Last edited by HallsofIvy; January 14th 2014 at 07:11 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. logarithmic equation
    Posted in the Algebra Forum
    Replies: 5
    Last Post: October 22nd 2012, 11:40 AM
  2. Logarithmic equation
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: August 21st 2010, 12:07 AM
  3. logarithmic equation
    Posted in the Algebra Forum
    Replies: 8
    Last Post: January 7th 2010, 12:12 AM
  4. Logarithmic equation help
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: February 13th 2009, 04:00 PM
  5. Logarithmic Equation Help
    Posted in the Business Math Forum
    Replies: 3
    Last Post: February 15th 2008, 04:32 PM

Search Tags


/mathhelpforum @mathhelpforum