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We have to compare 5^3125 and 10^20815^3125 = 5^2081* 5^1044 and 10^2081 = 5^2081 * 2^2081 --->5^1044 > 4^1044 = 2^2088 > 2^2081 ---> 5^3125 > 10^2081
2:45 Another shortcut for multiplying by 5 mentally is to multiply by 10 and divide by 2 (or the other way around).
5^3125 ? 10^2081 --> Dividing both sides by 5^2081 --> 5^1044 ? 2^2081 5^1044 > 4^1044 = 2^2088 > 2^2081 qed.
Shame on you, Cheater !
I had a feeling 5^5^5 would be the larger number, since it can be written as 5^3125. Usually the smaller base with the bigger exponent wins out.
Nice. We need to find an exception to that! 😜
Iits 5^ 1044 vs 4^ 1040.5. Obvious is result
That s no proof
@@Quest3669 No, he doesn't have to "apply [his] mind a bit." It's *not* obvious, and it's *not* a proof. You have no supporting steps. Write an English sentence. You need to delete your post, because it is *invalid.*
@@DieterSchütt from 5^ 1044 vs 4^ 1040.5 , divide both sides by 5^1040.5 . LHS =5 ^3.5 , RHS = (4/5)^1040.5 . LHS is more than 125 and RHS is < 1.
5^5 = 25x25x5=3125, 5^5^5 = 5^3125 = 125^(3125/3) AND 10^2081 = 100^(2081/2). 125 > 100 AND 3125/3 > 2081/2 since 3125x2 = 6250 > 2081x3 = 6243.So, 5^5^5 = 5^3125 > 5^3123 = (5^3)^1041 = 125^1041 > 100^1041 = (10^2)^1041 = 10^2082 > 10^2081.Therefore, 5^5^5 > 10^2081
5^3125or10^2081=2^2081*5^2081..5^1044or4^1044,5
Your exponent on the 4 at the end of the line is different from at least a couple of other similar approaches. Use a decimal point, not a comma.
LHS - RHS = 103.28...
It's simpler to do : 5^3125= 5^2081 *5^1044 and 10^2081=5^2081 *2^2081 and 2^2081=4^1040,5 then : it's easy to observe 5^1044 > 4^1040,5 .
Write the actual connecting step at the end, and use a decimal point, not a comma.
We have to compare 5^3125 and 10^2081
5^3125 = 5^2081* 5^1044 and 10^2081 = 5^2081 * 2^2081 --->
5^1044 > 4^1044 = 2^2088 > 2^2081 ---> 5^3125 > 10^2081
2:45 Another shortcut for multiplying by 5 mentally is to multiply by 10 and divide by 2 (or the other way around).
5^3125 ? 10^2081 --> Dividing both sides by 5^2081 --> 5^1044 ? 2^2081
5^1044 > 4^1044 = 2^2088 > 2^2081 qed.
Shame on you, Cheater !
I had a feeling 5^5^5 would be the larger number, since it can be written as 5^3125. Usually the smaller base with the bigger exponent wins out.
Nice. We need to find an exception to that! 😜
Iits 5^ 1044 vs 4^ 1040.5. Obvious is result
That s no proof
@@Quest3669 No, he doesn't have to "apply [his] mind a bit." It's *not* obvious, and it's *not* a proof. You have no supporting steps. Write an English sentence. You need to delete your post, because it is *invalid.*
@@DieterSchütt from 5^ 1044 vs 4^ 1040.5 , divide both sides by 5^1040.5 . LHS =5 ^3.5 , RHS = (4/5)^1040.5 . LHS is more than 125 and RHS is < 1.
5^5 = 25x25x5=3125, 5^5^5 = 5^3125 = 125^(3125/3) AND 10^2081 = 100^(2081/2). 125 > 100 AND 3125/3 > 2081/2 since 3125x2 = 6250 > 2081x3 = 6243.
So, 5^5^5 = 5^3125 > 5^3123 = (5^3)^1041 = 125^1041 > 100^1041 = (10^2)^1041 = 10^2082 > 10^2081.
Therefore, 5^5^5 > 10^2081
5^3125or10^2081=2^2081*5^2081..5^1044or4^1044,5
Your exponent on the 4 at the end of the line is different from at least a couple of other similar approaches. Use a decimal point, not a comma.
LHS - RHS = 103.28...
It's simpler to do : 5^3125= 5^2081 *5^1044 and 10^2081=5^2081 *2^2081 and 2^2081=4^1040,5 then : it's easy to observe 5^1044 > 4^1040,5 .
Write the actual connecting step at the end, and use a decimal point, not a comma.