Results 1 to 4 of 4

Math Help - logarithm problem

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    30

    logarithm problem

    Show that for any positive numbers x and a (with x not equal to 1) \log_{x^2} a = \frac{1}{2} \log_{x} a .

    Also, generalize the assertion in the problem above to powers other than  x^2 .




    Thank you (:
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2008
    Posts
    461
    Hi.


    Quote Originally Posted by meiyukichan View Post
    Show that for any positive numbers x and a (with x not equal to 1) \log_{x^2} a = \frac{1}{2} \log_{x} a .

    Also, generalize the assertion in the problem above to powers other than  x^2 .

    Do you know this rule: log_(y)x = \frac{ln(x)}{ln(y)} (rule1)?

    In this case \log_{x^2} a = \frac{ln(a)}{ln(x^2)} = \frac{1}{2}\frac{ln(a)}{ln(x)}

    because (rule2) log(x^n) = n log(x)

    Using (rule1)
    1/2 * log_x(a)

    Do you know these rules or do you have to proove them?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2008
    Posts
    30
    Quote Originally Posted by Rapha View Post
    Hi.





    Do you know this rule: log_(y)x = \frac{ln(x)}{ln(y)} (rule1)?

    In this case \log_{x^2} a = \frac{ln(a)}{ln(x^2)} = \frac{1}{2}\frac{ln(a)}{ln(x)}

    because (rule2) log(x^n) = n log(x)

    Using (rule1)
    1/2 * log_x(a)

    Do you know these rules or do you have to proove them?
    Now that you mentioned it, I recognize these rules and it helps with the first problem. I understand it now.
    Thank you! (:
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,577
    Thanks
    1418
    The rule follows from:

    If \log_{x^2} a= y, then a= (x^2)^y= x^{2y} so \log_x a= 2y and y= \log_{x^2} a= \frac{1}{2}\log_x a
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Logarithm problem
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: May 30th 2009, 04:18 AM
  2. help with this logarithm problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 6th 2008, 05:07 PM
  3. LOgarithm proBLeM
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: November 30th 2008, 04:50 AM
  4. logarithm problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: September 30th 2008, 05:02 PM
  5. Please help logarithm problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: April 1st 2006, 09:32 PM

Search Tags


/mathhelpforum @mathhelpforum