Results 1 to 6 of 6

Thread: laws of logarithms

  1. October 28th 2006, 08:19 AM #1
    Yogi_Bear_79
    Yogi_Bear_79 is offline
    Junior Member
    Joined
    Aug 2006
    Posts
    30

    laws of logarithms

    Please help with this example to apply the laws of logarithms to simplify the function f(x) =ln \sqrt\frac{9-x^2}{4+x^2}. Then find it’s derivative.
    Follow Math Help Forum on Facebook and Google+
  2. October 28th 2006, 08:27 AM #2
    Quick
    Quick is offline
    MHF Contributor Quick's Avatar
    Joined
    May 2006
    From
    New England
    Posts
    1,024
    Quote Originally Posted by Yogi_Bear_79 View Post
    Please help with this example to apply the laws of logarithms to simplify the function f(x) =ln \sqrt\frac{9-x^2}{4+x^2}. Then find it’s derivative.
    I can't help you with the derivative, but here's the simply part:

    you have: \ln\sqrt{\frac{9-x^2}{4+x^2}}

    rewrite: \ln\left(\left(\frac{9-x^2}{4+x^2}\right)^{\frac{1}{2}}\right)

    Thus: \frac{1}{2}\ln\frac{9-x^2}{4+x^2}

    rewrite: \frac{1}{2}\ln\frac{(3+x)(3-x)}{4+x^2}

    It is possible to go farther but I don't know how that might help...
    Follow Math Help Forum on Facebook and Google+
  3. October 28th 2006, 08:35 AM #3
    Soroban
    Soroban is offline
    Super Member
    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,429
    Thanks
    490
    Hello, Yogi_Bear_79!

    Do you know the Laws of Logarithms?

    Apply the laws of logarithms to simplify the function f(x) = \ln\sqrt\frac{9-x^2}{4+x^2}
    Then find its derivative.

    We have: . f(x) \;= \;\ln\sqrt{\frac{9-x^2}{4+x^2}} \:=\:\ln\!\left(\frac{9-x^2}{4+x^2}\right)^{\frac{1}{2}} \;=\;\frac{1}{2}\cdot\ln\!\left(\frac{9-x^2}{4+x^2}\right)

    Then: . f(x)\;=\;\frac{1}{2}\bigg[\ln(9-x^2) - \ln(4 + x^2)\bigg]


    Now differentiate it . . .
    Follow Math Help Forum on Facebook and Google+
  4. October 28th 2006, 08:37 AM #4
    Quick
    Quick is offline
    MHF Contributor Quick's Avatar
    Joined
    May 2006
    From
    New England
    Posts
    1,024
    Quote Originally Posted by Soroban View Post




    Then: . f(x)\;=\;\frac{1}{2}\bigg[\ln(9-x^2) - \ln(4 + x^2)\bigg]

    Wait, so \log\frac{a}{b}=\log a-\log b? That's useful...
    Follow Math Help Forum on Facebook and Google+
  5. October 28th 2006, 12:23 PM #5
    topsquark
    topsquark is offline
    Moderator
    topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,617
    Thanks
    291
    Awards
    1
    MHF Donor
    Quote Originally Posted by Quick View Post
    Wait, so \log\frac{a}{b}=\log a-\log b? That's useful...
    Yes it's true and yes it's useful!

    -Dan
    Follow Math Help Forum on Facebook and Google+
  6. October 28th 2006, 01:04 PM #6
    earboth
    earboth is offline
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,766
    Thanks
    99
    Quote Originally Posted by Quick View Post
    ...That's useful...
    Hi,

    I've attached a pdf-file with the logarithm rules and the corresponding power rules. Maybe this is useful for you too.

    EB
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+
« finding roots | Integral: Verify Anwser Please »

Similar Math Help Forum Discussions

  1. laws of logarithms
    Posted in the Algebra Forum
    Replies: 5
    Last Post: December 17th 2009, 03:28 AM
  2. Laws of logarithms
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 17th 2009, 01:49 PM
  3. Using laws of Logarithms
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 11th 2009, 07:54 PM
  4. Laws of Logarithms
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 9th 2007, 08:59 PM
  5. Laws of Logarithms
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 21st 2007, 06:48 PM

Search Tags


/mathhelpforum @mathhelpforum