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Math Help - conversion of log to the base of 4 to log to the base of 2

  1. #1
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    conversion of log to the base of 4 to log to the base of 2

    i know that log to the base of a of b can be re-written as (log of b)/(log of a)
    But, i got lost when i saw a question
    log to the base of 16 (x) + log to the base of 4 (x) + log to the base of 2 (x) = 7

    how would you go about solving this question?
    I thought about re-defining every single term of those logs in to (log of b)/(log of a) shape, but it doesnt give me a whole number answer (answer is 16)
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  2. #2
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    If you use LaTex it is a lot easier to read.
    [tex]\log_{16}(x)[/tex] gives \log_{16}(x).
    [tex]\frac{\log_{16}(x)}{\log_2(x)}[/tex] gives \frac{\log_{16}(x)}{\log_2(x)}.
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  3. #3
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    Thanks for the info, i will rewrite it to make it more clear
    \log_{16}(x) + \log_{4}(x)+ \log_{2}(x) = 7
    i couldnt find x (the hint in the book says i should be able to change \log_{16}(x) and \log_{4}(x) to the \log_{2}(x) form
    but i cant do that.
    how should i make that happen?
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  4. #4
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    \log_{16}(x)=\frac{\log(x)}{\log(16)}=\frac{\log(x  )}{4\log(2)}=\frac{1}{4}\log_2(x).
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  5. #5
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    thank you so much.
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