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Math Help - Logarithms...ugh

  1. #1
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    Mar 2008
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    Logarithms...ugh

    I need to rearrange this:
    log x + log y = z

    to prove that
    z = log xy

    I've managed to get to:
    x = 10(raised to) z - log y

    Don't know if I'm going in the right direction, or where to go from there
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  2. #2
    Senior Member topher0805's Avatar
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    This is a rule of logarithms:

    \log {a} + \log {b} = \log {ab}


    Pretty straight forward.
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  3. #3
    Senior Member
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    \log_b(xy) = \log_b(x) + \log_b(y) \!\, because b^x \cdot b^y = b^{x + y} \!\,
    From Wikipedia

    In detail:

    b^{\log_bx}=x,\enspace b^{\log_by}=y\rightarrow b^{\log_bx+\log_by}=xy=b^{\log_b(xy)}
    Last edited by james_bond; March 27th 2008 at 12:49 PM.
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