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Math Help - Prove logarithmic formula is accurate

  1. #1
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    Prove logarithmic formula is accurate

    Hi everyone
    I am trying to solve this question
    Prove that
    LOG4X=LOG2√X

    Thanks in advance
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Prove logarithmic formula is accurate

    Hint: prove the identity:

    \log_{a^n}(b)=\frac{\log_a(b)}{n}

    with the change of base formula:

    \log_a(c)=\frac{\log_b(c)}{\log_b(a)}
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  3. #3
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    Re: Prove logarithmic formula is accurate

    Thanks for the quick reply.
    What I understood is that I should treat it as change base of log4x to base 2
    Though I am sure you are pointing me in the correct direction my brain is dead after looking at this for the past 2 hours
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Prove logarithmic formula is accurate

    Yes, a more specific way to go would be to write:

    \log_4(a)=\frac{\log_2(a)}{\log_2(4)}=\frac{\log_2  (a)}{\log_2(2^2)}=...
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    Re: Prove logarithmic formula is accurate

    Thanks, nice car by the way
    What confuses me is the square root if I follow through the equation I feel I will still end up with an incorrect fraction
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  6. #6
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    Re: Prove logarithmic formula is accurate

    it is a rule of logarithms that:

    logn(ab) = b(logn(a)), even when b = 1/2.....
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    Re: Prove logarithmic formula is accurate

    Quote Originally Posted by lostinlalaland View Post
    Hi everyone
    I am trying to solve this question
    Prove that
    LOG4X=LOG2√X
    post basic log problems in the pre-university algebra forum ... this is not an advanced algebra problem.
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  8. #8
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    Re: Prove logarithmic formula is accurate

    See the image for solution
    Attached Thumbnails Attached Thumbnails Prove logarithmic formula is accurate-temp_delete.png  
    Last edited by ibdutt; December 19th 2012 at 12:53 AM.
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  9. #9
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    Re: Prove logarithmic formula is accurate

    Why bother with change of base ? You don't need it, (and I always struggle to remember it anyway, I finish up having to look it up to be sure I'm remembering it correctly).

    Let \log_{4}X=m, \text{  then  } X=4^{m}............(1)

    Let \log_{2}\sqrt{X}=n, \text{  then  } \sqrt{X}=2^{n} \Rightarrow X=4^{n}............(2)

    Comparison of (1) and (2) shows that m=n.
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