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Math Help - Solve for X... I Think I Did...?

  1. #1
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    Solve for X... I Think I Did...?

    The question Logx(X^5) = 5

    The first x is sub-script.

    I have:

    1) Logx(X^5) = 5
    2) X^5 = X^5
    3) x = x

    I imagine I'm wrong, as it seemed to easy. Where, if I did, go wrong? Thanks.
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  2. #2
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    Quote Originally Posted by iwanttogotouni View Post
    The question Logx(X^5) = 5

    The first x is sub-script.

    I have:

    1) Logx(X^5) = 5
    2) X^5 = X^5
    3) x = x

    I imagine I'm wrong, as it seemed to easy. Where, if I did, go wrong? Thanks.
    Does x = X?

    If so then answer number one is correct and I'd not write it any more than that. The rules explaining this are below

    \log_a(a) = 1

    \log_a(a^k) = k\,log_a(a) = k
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  3. #3
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    So:

    x = 1?

    And was "Does x = X," a rhetorical question, or are you asking about the difference of the two x's?

    Edit: Is k in the second equation, or do they just look together because they jumbled up?
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  4. #4
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by iwanttogotouni View Post
    So:

    x = 1?

    And was "Does x = X," a rhetorical question, or are you asking about the difference of the two x's?
    No, x is not 1. This is because of domain restrictions on the logarithm's base

    log_a(b) = c is equivalent to b = a^c

    a cannot be one because 1 raised to any power is always 1


    There are infinitely many values of x.

    x \in \mathbb{R} \, \, , \: x > 0 \, \, , \, \, x \neq 1

    No doubt someone else knows better notation than me for that - what it says is that x can be any real number greater than 0 which is not 1.

    x = \sqrt{e \pi} is a valid solution for example


    edit: about the X and x I was asking because they are generally taken as different variables although if they were different there'd be no way of solving the equation.

    edit 2: the k is just being used as an example to demonstrate the log power law, it is unrelated to the question you ask. k is often used to denote a constant
    Last edited by e^(i*pi); March 13th 2010 at 10:12 AM. Reason: typo
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  5. #5
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    two methods I know:
    Method 1
    log(x^5) = 5
    x^(log(x^5) = x^5
    x^5 = x^5 which is true for all x

    Method 2
    log(x^5) = 5
    5log(x) = 5
    5=5 which also is true (seems like an ugly "proof"? what can I do in order to make it look more sweet?)
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  6. #6
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    Oh, crap, I read it wrong. You mean step one is right? When you said answer, I kind of differentiated.
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  7. #7
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    e^(i*pi)'s Avatar
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    Yeah, step 1 is fine. It's a common result so would require no further working in a question
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  8. #8
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    Ok, thank-you very much. Sorry, I can be a literal person at times; I often over-analyze things.
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