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Math Help - Log equations - no solution?

  1. #1
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    Log equations - no solution?

    In the answers, it says these two don't have any solutions. I don't understand how, though.

    log(v-2) = 1 +log(v+2)
    and
    2 + logx = log(x-9)

    For the first one, I did:
    log(v-2/v+2) = 1
    v-2/v+2 = 10
    v-2 = 10v + 20
    0 = 9v + 22
    So I didn't get no solution. I don't know if this is right, though.

    For the second one, I did:
    2 = log(x-9) - logx
    2 = log(x-9/x)
    100 = x-9/x
    100x = x-9
    99x = -9
    Same thing with this one.
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  2. #2
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    Solve for x and v and then check the domain of log.
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  3. #3
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    pickslides's Avatar
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    Your answers for v and x will give you a negative value, what is a log's domain?
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  4. #4
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    e^(i*pi)'s Avatar
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    Your workings are fine. However, it is correct that there are no solutions because of the domain restrictions.

    f(a) = \log[a] is only valid for [/tex]a>0[/tex]

    In your first equation v-2 > 0 \implies v > 2

    In your second equation x-9 > 0 \implies x > -9

    If you check your solution against the domain restriction you'll find the values are not in the domain so there are no solutions
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  5. #5
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    Thank you.
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  6. #6
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