Mark:
If n > k, then is k^n bigger, or is n^k?
Well, that depends.
What sort of answer is that???.......
As it happens - the right one!!!
(Mark continues)
If 0 < k < n <e> k^n.
If e <= k < n, then n^k < k^n.
If 0 < k < e < n, then it depends on k and n.
It seems that in most cases a larger exponent creates a larger number, but not always.
2^3 is greater than 3^2
(2.5)^2 is less than 2^(2.5)
30.00001^30 is less than 30^(30.00001), etc.
It seemed to be that the larger exponent returned the larger number in every case with a few exceptions. I could not, however, figure out the "rule" to know what the exceptions are.
For example, we can tell graphically that 2^1000000 is greater than 1000000^2, but why? Is there a general rule about this?
It turns out that it's not easy to determine which will be larger.
If we can take the inequality
a^b > b^a
and raise each side to the 1/(ab) power, which will not change the inequality as long as we are only using positive numbers:
(a^b)^[1/(ab)] > (b^a)^[1/(ab)]
a^[b/(ab)] > b^[a/(ab)]
a^(1/a) > b^(1/b)
Thus the power with x as the base will be larger when x^(1/x) is larger.
Nice one Mark.
Miss mi our Southern Belle writes from her plantation,
"Would love a beer! Where's the Red Rooster anyway?"
Today, Red Rooster has over 360 stores and employs around 5000 staff across Australia. Just ask Dutchy...
TTH writes in support of others while failing to mention her own troubles, which were caused when a neighbors tree came crashing down in her yard. Had she been outside by the pool applying oil over her hot suntanned body; the results could have been hard to imagine (but I will give it a go).
YKW AKA Squirrel Nutkin writes, "ARE YOU NUTS!~"
If I may quote Mark, "Well, that depends."
"Try i am going to make you my (ykw's) Husband"
Just don't put me down on any tax return, the IRS want to hang me out to dry.
"(main frames). o.k.?"
Sure, whatever!
You know who continued,
"i'm lethargic and can't snap out of it!"
Have you been dressing up in latex again?
LE
VE
L
BLAME BLAME WHO'S
PERSON
ALITY
(main frames). o.k.? 
.
