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Math Help - Need help with Log please

  1. #1
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    Need help with Log please

    Hi I am having a hard time understanding logs in class can someone help?

    1.
    I am to find the exact value for this
    How would I start

    2^log base2 7

    Am i to transform this somehow first?


    2.Another one is logbase6 6^74 for this one I got a 74 it is right but why? its juse the exponent of the 6
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  2. #2
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    Quote Originally Posted by Jenne View Post
    Hi I am having a hard time understanding logs in class can someone help?

    1.
    I am to find the exact value for this
    How would I start

    2^log base2 7

    Am i to transform this somehow first?


    2.Another one is logbase6 6^74 for this one I got a 74 it is right but why? its juse the exponent of the 6
    log_2 7 is the real x such as 2^x = 7
    Therefore 2^{log_2 7} = 7

    In the same way
    log_6 {6^{74}} is the real x such as 6^x = 6^{74}
    Therefore log_6 {6^{74}} = 74
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by Jenne View Post
    Hi I am having a hard time understanding logs in class can someone help?

    1.
    I am to find the exact value for this
    How would I start

    2^log base2 7

    Am i to transform this somehow first?
    b^{\log_bx}=x

    2^{\log_27}=7

    Quote Originally Posted by Jenne View Post
    2.Another one is logbase6 6^74 for this one I got a 74 it is right but why? its juse the exponent of the 6
    \log_b b^x=x

    \log_6 6^{74}=74

    Just some more properties of logarithms. See here: Logarithmic Properties
    Enjoy.
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