Results 1 to 5 of 5

Math Help - Logarithmic Expression

  1. #1
    Newbie
    Joined
    Jul 2012
    From
    Third planet from the sun
    Posts
    1

    Logarithmic Expression

    How would this be simplified?

    Logarithmic Expression-logarithm.png

    I understand what would be done if the base on the logarithm were 9 but what happens in a case like this?
    Any help would be greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,561
    Thanks
    785

    Re: Logarithmic Expression

    Use the fact that (x^a)^b=(x^b)^a=x^{ab}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,832
    Thanks
    1602

    Re: Logarithmic Expression

    Quote Originally Posted by Pernello View Post
    How would this be simplified?

    Click image for larger version. 

Name:	logarithm.PNG 
Views:	3 
Size:	2.4 KB 
ID:	24350

    I understand what would be done if the base on the logarithm were 9 but what happens in a case like this?
    Any help would be greatly appreciated.
    \displaystyle \begin{align*} 9^{\log_3{20}} &= \left(3^2\right)^{\log_3{20}} \\ &= 3^{2\log_3{20}} \\ &= 3^{\log_3{\left(20^2\right)}} \\ &= 20^2 \\ &= 400 \end{align*}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie Neeraj's Avatar
    Joined
    Jul 2012
    From
    India
    Posts
    7

    Re: Logarithmic Expression

    Logarithmic Expression-logarithmic.jpg


    see formula in image, so that u can clear what is the answer
    9 log3 20 = 20 log3 9
    = 20 log3 (32)
    = 20 2 log 33
    = 20 2 *1
    =20 2 = 400
    Last edited by skeeter; July 26th 2012 at 07:46 AM. Reason: deleted link
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,173
    Thanks
    74

    Re: Logarithmic Expression

    x = log(3)20 = log(20) / log(3) ; 9^x = ?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: May 1st 2012, 10:54 AM
  2. Replies: 6
    Last Post: October 6th 2011, 02:48 PM
  3. Expand logarithmic expression
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: November 1st 2009, 11:37 AM
  4. Simplify logarithmic expression?
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 8th 2009, 12:36 PM
  5. Logarithmic expression
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: November 25th 2008, 03:26 PM

Search Tags


/mathhelpforum @mathhelpforum