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Math Help - logarithms equation

  1. #1
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    logarithms equation

    how do you prove that? (see the image)
    how would you simplify the left side to show it equals the right?
    logarithms equation-mathhelp.jpg
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  2. #2
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    Re: logarithms equation

    Hint:  \log_a b  \times \log _b a  = 1, so  \frac 1 {\log _a b} = \log _b a
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    Re: logarithms equation

    Quote Originally Posted by rgchel View Post
    how do you prove that? (see the image)
    how would you simplify the left side to show it equals the right?
    Click image for larger version. 

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    Here is a second way of looking at it.

    Because $\log_b(x)=\dfrac{\log(x)}{\log(b)}$ then $(\log_3(x))^{-1}=\dfrac{\log(3)}{\log(x)}$

    Now on the LHS we have a common denominator.
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