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Math Help - Change-of-Base Formula

  1. #1
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    Change-of-Base Formula

    Use the change-of-base formula and a calculator to evaluate each logarithm.

    (1) log_5 (18)

    (2) log_π (sqrt{2})

    Note: The symbol π stands for pi.
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  2. #2
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    the change of base formula is usually used to change to log base 10 or log base e because those are the log keys available on most calculators.

    to change from base "b" to base 10 or base e ...

    \log_b(x) = \frac{\log(x)}{\log(b)} = \frac{\ln(x)}{\ln(b)}

    get out your calculator and try it.
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  3. #3
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    Are you...

    In the questions given, b represents base 5 and pi and x represents 18 and sqrt{2}. Is this what you are saying?

    Are you also saying that log(x)/log(b) is the same as written ln(x)/ln(b)?

    Then I just plug and chug, right?

    Should I then round off the answers to the second or third decimal places? Which one?
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  4. #4
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    Quote Originally Posted by magentarita View Post
    In the questions given, b represents base 5 and pi and x represents 18 and sqrt{2}. Is this what you are saying? Mr F says: In your question 1, b = 5 and x = 18. In your question 2, b = n and x = sqrt{2}. I don't know where you have got pi from.

    Are you also saying that log(x)/log(b) is the same as written ln(x)/ln(b)? Mr F says: Yes s/he is.

    Then I just plug and chug, right? Mr F says: Yes.

    Should I then round off the answers to the second or third decimal places? Which one? Mr F says: Impossible to answer. The original question should state what accuracy is required.
    In fact, \log_b(x) = \frac{\log_a (x)}{\log_a (b)}for any base a > 0 and a \neq 1.
    Skeeter stated the formula for when you change to base 10 or base e - this is because you have to calculate a numerical value and even a scientific calculator has a log base 10 and log base e button.
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  5. #5
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    There is pi...

    This is the exact question 2 as given in the textbook:

    log_pi (sqrt{2})

    How do you solve that when there is pi in the question itself?
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  6. #6
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    \pi is just a number ... treat it as you would any other constant.
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  7. #7
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    pi is just a number

    Thanks
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