Results 1 to 5 of 5

Math Help - Logarithmic equation with different bases

  1. #1
    Newbie
    Joined
    Sep 2013
    From
    Dublin, Ireland
    Posts
    7

    Logarithmic equation with different bases

    Would appreciate some guidance on the problem below:

    Solve Log[base 25](6x + 25) + Log[base 5](x + 25) = 5, x a Natural number

    To solve I tried converting to a single base using Log[base A]x = Log[base B]x / Log[base B]A which gives:

    Log[base 25](6x + 25) = Log[base 5](6x + 25) / Log[base 5]25 = Log[base 5](6x+25) / 2

    So the equation becomes:

    Log[base 5](6x + 25) / 2 + Log[base 5](x + 25) = 5

    Log[base 5](6x + 25) + 2Log[base 5](x + 25) = 10

    Log[base 5](6x + 25) + Log[base 5](x + 25)^2 = 10

    Log[base 5](6x + 25)(x + 25)^2 = 10

    5^10 = (6x +25)(x +25)^2

    This seems like a nasty polynomial to solve - is there a simpler approach to the problem?

    Thanks in advance
    Corbomite1
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,404
    Thanks
    1293

    Re: Logarithmic equation with different bases

    No that is exactly what you have to do.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2013
    From
    Dublin, Ireland
    Posts
    7

    Re: Logarithmic equation with different bases

    OK, thanks!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1

    Re: Logarithmic equation with different bases

    Quote Originally Posted by corbomite1 View Post
    Would appreciate some guidance on the problem below:
    Solve Log[base 25](6x + 25) + Log[base 5](x + 25) = 5, x a Natural number
    Here is some advice on notation.
    You can learn to post symbols. It really is so easy. And it makes most of us more willing to find out how to help.
    This subforum will help you with the code. Once you begin, you quickly learn the code.

    [TEX]\log_{25}(6x+25)+\log_{5}(x+25)=5 [/TEX] gives  \log_{25}(6x+25)+\log_5(x+25)=5
    If you click on the “go advanced tab” you should see \boxed{\Sigma} on the tool-bar. That gives the [TEX]..[/TEX] wrap. Your LaTeX code goes between them.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2013
    From
    Dublin, Ireland
    Posts
    7

    Re: Logarithmic equation with different bases

    Understood, will do, thanks!

    So the problem would read \log_{25}{(6x+25)} + log_5{(x+25)}=5
    Last edited by corbomite1; September 25th 2013 at 03:11 AM. Reason: Amendment
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving Equation: Exponent with different bases
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: March 16th 2013, 07:11 AM
  2. Exponential equation with difforent bases question
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: December 3rd 2012, 06:12 AM
  3. Logarithmic Equation
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: May 10th 2010, 01:55 AM
  4. Solving a logarithmic equation with unlike bases.
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: April 4th 2010, 11:27 AM
  5. Logarithmic equation
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: September 11th 2009, 12:40 PM

Search Tags


/mathhelpforum @mathhelpforum