SOLUTION: Of the numbers in the set {3^5000,4^4000,5^3000,6^2000,7^1000}, which is the largest?

Algebra ->  Exponents -> SOLUTION: Of the numbers in the set {3^5000,4^4000,5^3000,6^2000,7^1000}, which is the largest?      Log On


   

Question 1133646: Of the numbers in the set {3^5000,4^4000,5^3000,6^2000,7^1000}, which is the largest?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

in the set {3^5000,4^4000,5^3000,6^2000,7^1000}
rewrite 4%5E4000 as %282%5E2%29%5E4000=2%5E8000
{3^5000,2^8000,5^3000,6^2000,7^1000}
compare exponents:
8000%3E5000%3E3000%3E2000%3E1000
=>4%5E4000 is largest
check:
3%5E%285000%29=4.0389976297871553397%2A+10%5E2385-> compare exponents again
4%5E%284000%29=1.73766203193809456+%2Ahighlight%2810%5E2408%29
5%5E%283000%29=8.12854862555773544%2A10%5E2096
6%5E%282000%29=2.0067846354902095384%2A+10%5E1556
7%5E%281000%29=1.2532566399657183181%2A+10%5E845