Logic-Based Comparison: Determining the Larger Number between 2^1000 and 500!

[barneygumble742]

hi...how can i tell which number is larger just from using logic?

for example a question says "which is larger 2^1000 or 500!?" the answer is 500! and the hint is: just compare the 500 factors appearing in each expression. i don't understand the hint but more importantly, I'm just not seeing the logic part of it.

thanks,
barneygumble742

 

[selfAdjoint]

Are you sure you copied this right? Because 2^1000 > 1000^100 > 500.

 

[barneygumble742]

that's not 500 exclamation point. it's 500 factorial. should i have used a different notation?

 

[neurocomp2003]

make 2^1000 into 500 factors and compare the factors is what the hint is suggesting
2^1000=(2^2)^500. and then compare it to 500 factors of 500!