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Math Help - Logarithms: Evalute or simplify

  1. #1
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    Logarithms: Evalute or simplify

    Evaluate or simplify



    5^(3log57)
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  2. #2
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    Use 2 log laws.

    a\log_bc = \log_bc^a

    then

    a^{\log_ab^c} = b^c
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  3. #3
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    Quote Originally Posted by danielh9103 View Post
    Evaluate or simplify



    5^(3log57)
    Simplifying..

    5^y=x\ \Rightarrow\ y=log_5x

    3log_57=log_5x

    log_5\left(7^3\right)=log_5x
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  4. #4
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    @Archie Meade

    i feel it can be simplified more... or is that the final answer?

    obviously you can simplify 7^3 or would that be incorrect?
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  5. #5
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    Quote Originally Posted by habibixox View Post
    @Archie Meade

    i feel it can be simplified more... or is that the final answer?

    obviously you can simplify 7^3 or would that be incorrect?
    Yes, habibixox,

    just evaluating that power gives the very final value of x, the last calculation required,
    but that preceding piece is all that is required to say goodbye to the logarithm part.
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