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Math Help - Another logarithmic question

  1. #1
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    Another logarithmic question

    Sorry please help me.with another one, how should I do lg(x-2)=(lg3)^2. Thanks really much!
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  2. #2
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    Re: Another logarithmic question

    The notation \lg is not familiar to me (I don't know for sure which base is implied), but I would write:

    \lg(x-2)=\lg(3)\lg(3)

    Now, on the right, use the property c\cdot\log_a(b)=\log_a(b^c). What do you find?
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  3. #3
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    Re: Another logarithmic question

    Thanks sir! lg is log10, has a base 10. but isn't the property you suggested only for one lg? In this case there's two, (lg3)(lg3).
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  4. #4
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    Re: Another logarithmic question

    Quote Originally Posted by MarkFL2 View Post
    The notation \lg is not familiar to me (I don't know for sure which base is implied), but I would write:

    \lg(x-2)=\lg(3)\lg(3)

    Now, on the right, use the property c\cdot\log_a(b)=\log_a(b^c). What do you find?
    You would only be able to use this property if the right hand side was \displaystyle \begin{align*} \log{(3)} + \log{(3)} = 2\log{(3)} = \log{\left( 3^2 \right)} \end{align*}, NOT \displaystyle \begin{align*} \log{(3)} \log{(3)} = \left[ \log{(3)} \right]^2 \mathbf{\neq} \log{\left( 3^2 \right)} \end{align*}.

    To solve this equation...

    \displaystyle \begin{align*} \log{(x - 2)} &= \left[ \log{(3)} \right]^2 \\ x - 2 &= 10^{\left[ \log{(3)} \right]^2} \\ x &= 10^{\left[ \log{(3)} \right]^2} + 2 \end{align*}
    Last edited by Prove It; November 23rd 2012 at 05:14 AM.
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  5. #5
    MHF Contributor MarkFL's Avatar
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    Re: Another logarithmic question

    I was suggesting to write:

    \lg(x-2)=\lg\left(3^{\lg(3)} \right)

    x-2=3^{\lg(3)}

    x=2+3^{\lg(3)}
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