TITLE: Which of the following powers is bigger: $2^{41}$ or $3^{24}$?
QUESTION [20 upvotes]: Calculate the maximum between the given numbers
 $$ \max(2^{41},3^{24})\text{.}$$ 
I got stuck when I tried to decompose the exponent as $41$ is a prime number.

REPLY [2 votes]: A definitive answer using log functions:
log(3) / log(2) = 1.58496
324 = (21.58496)24 = 21.58496 * 24 = 238.039
Therefore: 241 > 324