# How would you simplify this equation?

• August 11th 2010, 11:37 PM
Andre
How would you simplify this equation?
$c=\lceil\log_{\lceil2^\frac{a}{c}\rceil}2^a\rceil$
• August 11th 2010, 11:44 PM
Amer
$\lceil\log_{\lceil2^\frac{a}{c}\rceil}2^a\rceil$

u should know two things here

$\log a^b = b \log a$

$log_a a = 1$

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

$\lceil\log_{\lceil2^\frac{a}{c}\rceil}\left(2^{\fr ac{a}{c}}\right)^c\rceil=c\lceil\log_{\lceil2^\fra c{a}{c}\rceil}\left(2^{\frac{a}{c}}\right)\rceil=c (1)$
• August 12th 2010, 12:26 AM
Andre
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 $\log_{\lceil2^\frac{a}{c}\rceil}2^{\frac{a}{c}} = 1$.