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Thread: 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
    $\displaystyle log_2 7$ is the real x such as $\displaystyle 2^x = 7$
    Therefore $\displaystyle 2^{log_2 7} = 7$

    In the same way
    $\displaystyle log_6 {6^{74}}$ is the real x such as $\displaystyle 6^x = 6^{74}$
    Therefore $\displaystyle log_6 {6^{74}} = 74$
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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?
    $\displaystyle b^{\log_bx}=x$

    $\displaystyle 2^{\log_27}=7$

    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
    $\displaystyle \log_b b^x=x$

    $\displaystyle \log_6 6^{74}=74$

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