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    geobeeker's Avatar
    geobeeker Posts: 6, Reputation: 1
    New Member
     
    #1

    Feb 25, 2008, 01:49 PM
    solving an equation containing ln(x)
    I have f'(x) = x(2ln(x) - 3) / (ln(x) - 1)^2 (which matches my book's answer)

    My book says setting this equal to zero gives:

    2ln(x) - 3 = 0

    I think this implies that x / (ln(x) - 1)^2 equals 1
    or (ln(x) - 1)^2 = x
    but I don't understand why!

    I need to see the steps.

    Thanks,
    Mr_am's Avatar
    Mr_am Posts: 105, Reputation: 4
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    #2

    Feb 25, 2008, 05:40 PM
    if f'(x) is set to zero.. it implies x=o or 2ln(x)-3 is zero. Like saying A.B = zero means A is zero or B is zero. In this case A is x and 2ln(x)-3 is B. In this case we have A.B/C we are concerned with terms that make it zero.. obviously A or B being zero.
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
    Expert
     
    #3

    Feb 26, 2008, 07:54 AM
    Quote Originally Posted by geobeeker
    I have f'(x) = x(2ln(x) - 3) / (ln(x) - 1)^2 (which matches my book's answer)


    I think this implies that x / (ln(x) - 1)^2 equals 1
    or (ln(x) - 1)^2 = x
    but I don't understand why!
    Sorry, but if 2 ln(x) - 3 = 0, this does not imply that x / (ln(x) - 1)^2 equals 1. Why do you think it does?
    zenmeyang's Avatar
    zenmeyang Posts: 2, Reputation: 1
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    #4

    Mar 10, 2008, 08:13 PM
    If you say A.B / C = 0
    Implies A= 0 or B = 0 But C must not equal to zero.


    f'(x) = x(2ln(x) - 3) / (ln(x) - 1)^2 =0
    That means x = 0 or 2 ln(x) - 3 = 0.
    When x = 0, the denominator (ln(x) - 1)^2 also equal to 0.
    It forms a 0/0, it is undefined.
    That means x can't be zero.

    So the only value makes f'(x) zero is 2 ln(x) - 3 = 0.
    jasondelee's Avatar
    jasondelee Posts: 4, Reputation: 1
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    #5

    Feb 10, 2012, 11:52 PM
    if a/b=o it implies a=0 but this (a=0)doesn't mean b=1 or 1/b=1 .so b can be any number except 0.the value of b doesn't affect the equation.cause a=0*b=0 for any value of b.

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