# Math Help - How would you simplify this equation?

1. ## How would you simplify this equation?

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

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

u should know two things here

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

$log_a a = 1$

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

$\lceil\log_{\lceil2^\frac{a}{c}\rceil}\left(2^{\fr ac{a}{c}}\right)^c\rceil=c\lceil\log_{\lceil2^\fra c{a}{c}\rceil}\left(2^{\frac{a}{c}}\right)\rceil=c (1)$

3. 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 $\log_{\lceil2^\frac{a}{c}\rceil}2^{\frac{a}{c}} = 1$.