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Thread: simplify this log expression

  1. #1
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    simplify this log expression

    This is what I had:

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

    is this correct? can I simplify any further?

    thanks
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  2. #2
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    $\displaystyle \log_a(MN) = \log_aM+\log_aN
    $
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  3. #3
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    Quote Originally Posted by differentiate View Post
    This is what I had:

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

    is this correct? can I simplify any further?

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

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

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

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

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

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


    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 $\displaystyle e$.
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  4. #4
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    thanks a bunch Prove it!
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