Results 1 to 8 of 8

Math Help - Does (ln x)^2 = ln x^2?

  1. #1
    Member
    Joined
    Oct 2007
    Posts
    178

    Does (ln x)^2 = ln x^2?

    If it doesn't, what does it equal?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by Truthbetold View Post
    If it doesn't, what does it equal?
    No.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2007
    Posts
    178
    Lol! Equals 'no'. I'll take that as "simplifying it more will be overly difficult if not impossible, so don't bother."
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Truthbetold View Post
    Lol! Equals 'no'. I'll take that as "simplifying it more will be overly difficult if not impossible, so don't bother."
    all that's needed here is a counter example, try x = 2. you will realize you get different answers for each expression


    (\ln x)^2 = \ln x \cdot \ln x

    while \ln x^2 = 2 \ln |x| ....clearly these are not the same thing
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Dec 2007
    Posts
    11
    ln x^2 = 2lnx
    (lnx)^2 = (ln x)*(lnx)
    so no they are not equal (there may be a value for which they are but that would be a fluke
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member DivideBy0's Avatar
    Joined
    Mar 2007
    From
    Melbourne, Australia
    Posts
    432
    Quote Originally Posted by suissa View Post
    ln x^2 = 2lnx
    (lnx)^2 = (ln x)*(lnx)
    so no they are not equal (there may be a value for which they are but that would be a fluke
    x=1 or x=e^2, no fluke.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    GAMMA Mathematics
    colby2152's Avatar
    Joined
    Nov 2007
    From
    Alexandria, VA
    Posts
    1,172
    Awards
    1
    Quote Originally Posted by DivideBy0 View Post
    x=1 or x=e^2, no fluke.
    The OP was asking if they were equal, which assumes for all values of x, but it was a good idea to point that out for him/her.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,668
    Thanks
    298
    Awards
    1
    Quote Originally Posted by Truthbetold View Post
    If it doesn't, what does it equal?
    I would view this as an exercise in order of operations:
    lnx^2 = ln(x^2)
    by definition, and since ln is not a linear operator
    (ln(x))^2 \neq ln(x^2)

    -Dan
    Follow Math Help Forum on Facebook and Google+


/mathhelpforum @mathhelpforum