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Math Help - Urgent: LOG Test today please help

  1. #1
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    Urgent: LOG Test today please help

    Evaluate log 5 (1685) to eight decimal places.
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  2. #2
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    Hello, AFan!

    You are expected to know the Base-Change Formula
    . . and have a calculator.


    Evaluate \log_5(1685) to eight decimal places.

    Base-Change Formula: . \log_b(N) \;=\;\frac{\log(N)}{\log(b)} .
    using any base

    So we have: . \log_5(1685) \;=\;\frac{\ln 1685}{\ln 5} \;\approx\;\boxed{4.61622085}


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    Check: . 5^{4.61622085} \:=\:1685.000009\quad\hdots . close enough!

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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, AFan!

    You are expected to know the Base-Change Formula
    . . and have a calculator.



    Base-Change Formula: . \log_b(N) \;=\;\frac{\log(N)}{\log(b)} .
    using any base

    So we have: . \log_5(1685) \;=\;\frac{\ln 1685}{\ln 5} \;\approx\;\boxed{4.61622085}


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    Check: . 5^{4.61622085} \:=\:1685.000009\quad\hdots . close enough!

    How do you input that into the calculator, can anyone show me please,


     5^{4.61622085} = 1685.000009


    thanks!
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by hana_102 View Post
    How do you input that into the calculator, can anyone show me please,


     5^{4.61622085} = 1685.000009


    thanks!
    5^4.61622085
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