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Math Help - logarithm problem

  1. #1
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    logarithm problem

    Hi,

    I have a problem solving that equation logx sqrt 5 = -1/2 ... when i'm trying to solve I don't know what to do after I'm at that part of the equation x ^-1/2 = sqrt 5

    Thanks for the help

    Sebastien
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  2. #2
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    Re: logarithm problem

    Quote Originally Posted by sebastien View Post
    Hi,

    I have a problem solving that equation logx sqrt 5 = -1/2 ... when i'm trying to solve I don't know what to do after I'm at that part of the equation x ^-1/2 = sqrt 5

    Thanks for the help

    Sebastien
    Hang on, is this \displaystyle \begin{align*} \log{(x)}\sqrt{5} = -\frac{1}{2}  \end{align*} or \displaystyle \begin{align*} \log{(x\sqrt{5})} = -\frac{1}{2}  \end{align*} ?

    Also, what is the base of the logarithm?
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  3. #3
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    Re: logarithm problem

    The equation is log base x sqrt 5 = -1/2
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  4. #4
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    Re: logarithm problem

    Quote Originally Posted by sebastien View Post
    The equation is log base x sqrt 5 = -1/2
    \displaystyle \begin{align*} \log_x{\sqrt{5}} &= -\frac{1}{2} \\ \sqrt{5} &= x^{-\frac{1}{2}} \\ 5 &= x^{-1} \\ 5^{-1} &= x \\ x &= \frac{1}{5}  \end{align*}
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  5. #5
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    Re: logarithm problem

    thank you for the help
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