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Math Help - Ssimplifying Logs

  1. #1
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    Smile Ssimplifying Logs

    log base 5 of (8) * log base 64 of (25)


    Could someone show me the steps so I can apply it to my other hw problems.


    Thanks,
    Mr_GREEN
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  2. #2
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    Hello, Mr_Green!

    Are you allowed to use the Base-Change Formula?


    Simplify: . \log_5(8)\cdot\log_{64}(25)

    Using the Base-Change Formula, we have: . \frac{\log(8)}{\log(5)}\cdot\frac{\log(25)}{\log(6  4)}

    . . = \:\frac{\log(8)}{\log(5)}\cdot\frac{\log(5^2)}{\lo  g(8^2)} \:=\:\frac{\log(8)}{\log(5)}\cdot\frac{2\!\cdot\!\  log(5)}{2\!\cdot\!\log(8)} \:=\:1

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  3. #3
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by Soroban View Post
    Hello, Mr_Green!

    Are you allowed to use the Base-Change Formula?



    Using the Base-Change Formula, we have: . \frac{\log(8)}{\log(5)}\cdot\frac{\log(25)}{\log(6  4)}

    . . = \:\frac{\log(8)}{\log(5)}\cdot\frac{\log(5^2)}{\lo  g(8^2)} \:=\:\frac{\log(8)}{\log(5)}\cdot\frac{2\!\cdot\!\  log(5)}{2\!\cdot\!\log(8)} \:=\:1

    Wow, yet another convenient thing with logs. Does it convert the numbers to log_10?
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  4. #4
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    Quote Originally Posted by Quick
    Does it convert the numbers to log_10?

    It converts to any base: . \log_a(N) \;=\;\frac{\log_b(N)}{\log_b(a)}

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