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    LynnM's Avatar
    LynnM Posts: 34, Reputation: 2
    Junior Member
     
    #1

    Sep 2, 2010, 01:14 PM
    Exponential and Logarithmic Equations
    Hi. The question says to solve logx^{2} = (logx)^{2}.

    My brain tells me to do this:

    10^{logx^{2}} = 10^{logx} * 10^{logx}

    x^{2} = x * x

    x = x

    The text solution says that my brain is mistaken and the answer should be 1 or 0. Not too sure how to get that. I can see that they working by plugging them into the original equation but I can't figure out how to come up with them as answers.
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
    Uber Member
     
    #2

    Sep 3, 2010, 08:58 AM

    Lol, okay, let's try again.



    As I see it, it's not this easy to solve... so, let's make use of a substitution, that is, let:



    So? We first find all the log x.





    Now, let's use y = log x.



    Can you solve for y now? Once you get that, replace y again by log x. This time, you should get the answer. Post what you do! :)
    LynnM's Avatar
    LynnM Posts: 34, Reputation: 2
    Junior Member
     
    #3

    Sep 3, 2010, 09:40 AM

    Okay, I've got it! Here it goes:







    so... logx=0 and logx-2=0...





    and...





    yay!:)

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