Results 1 to 5 of 5

Math Help - Why logarithmic functions instead of radical functions?

  1. #1
    Newbie
    Joined
    Feb 2007
    Posts
    10

    What is the relationship between logarithms and radicals?

    Here's my question: what is the relationship between radicals and logarithms? How are they related?

    (My original question is below, but the answer occurred to me after I posted it)

    I have a simple question--why is the inverse of an exponential function a logarithmic function instead of a radical function?

    If F(x) = 5^x, wouldn't the inverse be x = 5^y, and couldn't that be written \sqrt[5]{x}? Why must it be written log_5x
    Last edited by shirkdeio; December 4th 2008 at 07:43 AM. Reason: new question
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Quote Originally Posted by shirkdeio View Post
    Here's my question: what is the relationship between radicals and logarithms? How are they related?

    (My original question is below, but the answer occurred to me after I posted it)

    I have a simple question--why is the inverse of an exponential function a logarithmic function instead of a radical function?

    If F(x) = 5^x, wouldn't the inverse be x = 5^y, and couldn't that be written \sqrt[5]{x}? Why must it be written log_5x
    Hi

    If y = 5^x then x = log_5 \,y

    If y = x^5 then x = \sqrt[5] y
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2007
    Posts
    10
    Quote Originally Posted by running-gag View Post
    Hi

    If y = 5^x then x = log_5 \,y

    If y = x^5 then x = \sqrt[5] y
    Thanks. I don't know why I had trouble with that--logarithms confuse me.

    But is y = 5^x the inverse of \sqrt[x]{y} = 5? If so, what is the relationship/difference between the radical and y = log_5{x}?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Quote Originally Posted by shirkdeio View Post
    Thanks. I don't know why I had trouble with that--logarithms confuse me.

    But is y = 5^x the inverse of \sqrt[x]{y} = 5? If so, what is the relationship/difference between the radical and y = log_5{x}?
    The inverse function of y=f(x) is x = f^{-1}(y)
    You have to express x function of y

    If y = 5^x then x = log_5\,y

    \sqrt[x]{y} = 5 is also true but it is not in the form x = f^{-1}(y)

    It is the same as per the example :
    If y = 5x then x = \frac{y}{5}

    \frac{y}{x} = 5 is also true but it is not in the form x = f^{-1}(y)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Feb 2007
    Posts
    10
    Thank you. I think I better understand logarithms now. I appreciate the help!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Logarithmic Functions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 11th 2009, 06:10 PM
  2. functions involving radical
    Posted in the Algebra Forum
    Replies: 4
    Last Post: March 24th 2009, 01:34 AM
  3. Find Inverse of Radical Functions
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: November 9th 2008, 05:24 AM
  4. Logarithmic Functions
    Posted in the Algebra Forum
    Replies: 2
    Last Post: July 18th 2008, 03:50 PM
  5. Replies: 19
    Last Post: June 5th 2006, 05:24 AM

Search Tags


/mathhelpforum @mathhelpforum