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Math Help - simplify this log expression

  1. #1
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    simplify this log expression

    This is what I had:

     \log _354 + log_35 - log_84
     log_33 + log_33 + log_32 + log_35 - log_8(8^\frac{2}{3})
     2\tfrac{1}{3} + log_310

    is this correct? can I simplify any further?

    thanks
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  2. #2
    Super Member bigwave's Avatar
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    \log_a(MN) = \log_aM+\log_aN<br />
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  3. #3
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    Quote Originally Posted by differentiate View Post
    This is what I had:

     \log _354 + log_35 - log_84
     log_33 + log_33 + log_32 + log_35 - log_8(8^\frac{2}{3})
     2\tfrac{1}{3} + log_310

    is this correct? can I simplify any further?

    thanks
    \log_3{54} + \log_3{5} - \log_8{4}

     = \log_3{(27 \cdot 2)} + \log_3{5} - \log_8{\left(8^{\frac{2}{3}}\right)}

     = \log_3{27} + \log_3{2} + \log_3{5} - \frac{2}{3}

     = \log_3(3^3) + \log_3{(2\cdot 5)} - \frac{2}{5}

     = 3 + \log_3{10} - \frac{2}{5}

     = \frac{13}{5} + \log_3{10}.


    So yes, you are correct. And no, it can't be simplified any further. The best you could do is to convert it to a base 10 or base e.
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  4. #4
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    thanks a bunch Prove it!
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