Question

write the numbers in order from least to greatest 2^100, 3^60,10^30, or 31^20

This is practice for a competition and I'm not allowed to use a calcultor so could you show a way to do it?

Answer 1

I'm trying to figure out a way to do this by hand. That is some pretty hard mental math. I'll snap a picture of my student software and show you why the solution works. I have to learn how to do this by hand too. I bet I'll be lucky enough (hint the sarcasm) to get this type of problem at both competitions I'll go to this year. The solution is: 2^(100)>10^(30)>31^(20)>3^(60)

Answer 2

@doulikepiecauseidont

Answer 3

Yeah, I got that on a CALCULATOR

Answer 4

Hey, I understand that. I don't need attitude because I could have left you up the creek without a paddle on this. I think that's what I'm going to do. I don't appreciate there being no appreciation for some kind of help or sympathy....

Answer 5

No, I was agreeing you, lol sorry maybe I should have put that at the end, I meant I'm at the same kind of situation that I can genreate it on a calculator but on the hand it's rather hard, sorry for the confusion

Answer 6

@bkeith2698 ? You there?

Answer 7

\(2^{100}=(2^{10})^{10}\\3^{60}=(3^6)^{10}\\10^{30}=(10^3)^{10}\\31^{20}=(31^2)^{10}\) so, just compare the core of the number
that cores can be written as \((2^5)^2\\(3^3)^2\\(10)^{(\frac{3}{2}})^2\\31^2\)

Answer 8

Maybe it'd help if we used logarithms?

Answer 9

Actually @Loser66 that makes it easier.

Answer 10

now, it's quite easy to compare the cores because
2^5 = 32
3^3 = 27
31 =31
just 10^(3/2) it's >31 and <32

Answer 11

Thanks