Results 1 to 2 of 2

Math Help - sum or differences of logs

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    17

    sum or differences of logs

    needing help with finding the sum or difference of the function:
    log_a x-y overthe square root of x^2-y^2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,905
    Thanks
    765
    Hello, bastropgarl!

    Note sure what you're asking for . . .


    needing help with finding the sum or difference of the function:

    . . . \log_a\left(\frac{x-y}{\sqrt{x^2-y^2}}\right)

    We have: . \log_a\left(\frac{x-y}{\sqrt{(x-y)(x+y)}}\right)

    . . . . . . . . =\;\log_a\left(\frac{x-y}{(x-y)^{\frac{1}{2}}(x+y)^{\frac{1}{2}}}\right)

    . . . . . . . . =\;\log_a\left(\frac{(x-y)^{\frac{1}{2}}}{(x+y)^{\frac{1}{2}}}\right)

    . . . . . . . . =\;\log_a\left(\frac{x-y}{x+y}\right)^{\frac{1}{2}}

    . . . . . . . . =\;\frac{1}{2}\log_a\left(\frac{x-y}{x+y}\right)

    . . . . . . . . = \;\frac{1}{2}\bigg[\log_a(x-y) - \log_a(x+y)\bigg]

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 9
    Last Post: February 22nd 2011, 06:39 PM
  2. sum and differences of logs
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 31st 2010, 11:17 AM
  3. first and second differences
    Posted in the Algebra Forum
    Replies: 5
    Last Post: August 8th 2008, 08:06 AM
  4. Dealing with Logs and Natural Logs
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: April 14th 2008, 07:18 AM
  5. several questions-logs/natural logs
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 12th 2007, 09:58 PM

Search Tags


/mathhelpforum @mathhelpforum