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

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Question 1066037: Of the numbers in the set { 3^5000, 4^4000, 5^3000, 6^2000, 7^1000}, the largest is:
Found 2 solutions by Boreal, MathTherapy:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
can take logs of these to compare
5000 log 3
4000 log 4
3000 log 5
2000 log 6
1000 log 7
A calculator could be used here, although log 3 is 0.4771, log 4 is 2 log 2 or 0.6026, log 6 is log 3+log 2 or 0.8084; log 5 + log2=log 10=1, so log 5 is 0.6987.
log 3/log 4 is 5000 (0.4771)/4000(0.6026), and log 4 is larger by comparison.
compare log 5/log 4 and have 3000(0.6987)/4000(.6026).
log 4 is larger
log 6 with log 4 is 2000 log 6/4000 log 4 or 1*0.8084/2*0.6026
4000 log 4 is the largest.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Of the numbers in the set { 3^5000, 4^4000, 5^3000, 6^2000, 7^1000}, the largest is:
You just need to get all expressions with the SAME EXPONENT, as follows:











Since all are raised to the same power (1,000) it’s extremely easy to determine which is largest. 

Besides, you can answer other questions related to size of each, and comparisons.

That's how simple this is!