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Math Help - log problem

  1. #1
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    log problem

    2 Log(X) + Log 0.1 = Log 5 + Log 2
    a a a a

    i got X= 10 , and -10
    i think all answers accepted because there is power 2 in 2 Log(X)so -10 won't be refused
    is that right????
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  2. #2
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    Re: log problem

    2 Log(X) + Log 0.1 = Log 5 + Log 2
    2logx = log (10/0.1)
    2logx = log100
    2logx = 2
    logx=1
    x=10.

    x cannot be -10 ,cause logy, y<0 ,is undefined
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  3. #3
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    Re: log problem

    note log is a function that have unique sol only if there is
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  4. #4
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    Re: log problem

    Quote Originally Posted by johnnylam123 View Post
    2 Log(X) + Log 0.1 = Log 5 + Log 2
    2logx = log (10/0.1)
    2logx = log100
    2logx = 2
    logx=1
    x=10.

    x cannot be -10 ,cause logy, y<0 ,is undefined
    ok but 2Log X = Log X^2
    so -10 will be 100 and Log 100 = 2???
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  5. #5
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    Re: log problem

    x=-10 would fail the original equation.
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  6. #6
    mfb
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    Re: log problem

    2Log X = Log X^2 is a formula for positive x only.
    In general, n\, log(|x|) = log(|x|^n)

    With complex numbers, you can evaluate log(-10) (it is a complex number), but you cannot use the formula given above, as -10 is not [real and] positive.
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  7. #7
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    Re: log problem

    Quote Originally Posted by mido22 View Post
    2 Log(X) + Log 0.1 = Log 5 + Log 2
    a a a a
    Is the actual problem 2\log_a(X)+\log_a(0.1)=\log_a(5)+\log_a(2)~?
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  8. #8
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    Re: log problem

    Quote Originally Posted by Plato View Post
    Is the actual problem 2\log_a(X)+\log_a(0.1)=\log_a(5)+\log_a(2)~?
    no it is without brackets
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  9. #9
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    Re: log problem

    Quote Originally Posted by mido22 View Post
    no it is without brackets
    What brackets?

    Are you talking parenthesis, (~)~?.
    If you are you need to know that it is incorrect to write \color{red}\log_a X.
    That is function notation. Just as we write f(x), we also write \log_a( X).
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  10. #10
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    Re: log problem

    even it is loga, results is the same
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