Taking a more manageable example, 5^2=25, 4^3=64. Since exponential functions increase monotonically, it can be inferred by induction that the smaller base with the larger exponent will be always be greater than the larger base with the smaller exponent
(1+1/n)^n=e is mistake if it's without limit. For example (1+1/2)^2=2.25, not e.
You are right. Though the proof can be salvaged by saying (1+1/n)^n
1.1^4
This works untill x=24.15…. after that 11^x is bigger then 10^(x+1)
Taking a more manageable example, 5^2=25, 4^3=64. Since exponential functions increase monotonically, it can be inferred by induction that the smaller base with the larger exponent will be always be greater than the larger base with the smaller exponent
So 2^2 > 10^1 ?
@@brendanward2991 no because 2^2 = 4 and 10^1 = 10 so 2^2 < 10^1
@@brendanward2991
And 2^2< 1^3 for sure...
by induction obviously
😂
11^11
1^1 ( n ➖ 1s+1).
This is a dumb question... Is it so hard to just count the amount of numbers on both sides?
10^12=(11-1)^12=10*(11^11+11^10+...+11+1) > 11^11
uhm... (11-1)^12 is not 10*(11^11+11^10+...). It is 10 * (11^11 - 11*11^10 + 55*11^9 - ...)
@@frarugi87 11*11^10 is 11^11
@@frarugi87 search for (x - 1)^n
@@rodicabrudea832 yes but it has a - sign in front of it, not a +
@@frarugi87 yes, I got your Point. You are right.