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Math Help - How would you simplify this equation?

  1. #1
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    How would you simplify this equation?

    c=\lceil\log_{\lceil2^\frac{a}{c}\rceil}2^a\rceil
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  2. #2
    MHF Contributor Amer's Avatar
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    Jordan
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    \lceil\log_{\lceil2^\frac{a}{c}\rceil}2^a\rceil

    u should know two things here

    \log a^b = b \log a

    log_a a = 1

    \lceil\log_{\lceil2^\frac{a}{c}\rceil}2^{\frac{ac}  {c}}\rceil

    \lceil\log_{\lceil2^\frac{a}{c}\rceil}\left(2^{\fr  ac{a}{c}}\right)^c\rceil=c\lceil\log_{\lceil2^\fra  c{a}{c}\rceil}\left(2^{\frac{a}{c}}\right)\rceil=c  (1)
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  3. #3
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    Thanks for your help. I really appreciate it; however, your solution has an error because it assumes \lceil2^\frac{a}{c}\rceil = 2^\frac{a}{c}. Since this is not true, then it's wrong to say \log_{\lceil2^\frac{a}{c}\rceil}2^{\frac{a}{c}} = 1.
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