What if there are an odd amount of things to do the exponential mean of? Then how would you do it?
What if you defined an exponential mean as a mean such that![[Image: png.image?\dpi%7B110%7D%20k%5E%7Bk%5E%7B\log_k(\log_...\log_k(b))]](https://latex.codecogs.com/png.image?\dpi%7B110%7D%20k%5E%7Bk%5E%7B\log_k(\log_k(a))+\log_k(\log_k(b)))
, For some k such as ![[Image: png.image?\dpi%7B110%7D%20\sqrt2]](https://latex.codecogs.com/png.image?\dpi%7B110%7D%20\sqrt2)
?
Then![[Image: png.image?\dpi%7B110%7D%20\text%7BExp-Mean3%7D(a,b)]](https://latex.codecogs.com/png.image?\dpi%7B110%7D%20\text%7BExp-Mean3%7D(a,b))
would equal ![[Image: png.image?\dpi%7B110%7D%20k%5E%7Bk%5E%7B\log_k(\log_...rt%5Ba%5D%7Bb%7D))]](https://latex.codecogs.com/png.image?\dpi%7B110%7D%20k%5E%7Bk%5E%7B\log_k(\log_k(\sqrt%5Bb%5D%7Ba%7D))+\log_k(\log_k(\sqrt%5Ba%5D%7Bb%7D)))
.
If a and are complex, then![[Image: png.image?\dpi%7B110%7D%20\text%7BExp-Mean3%7D(a...qrt%5Ba%5D%7Bb%7D)]](https://latex.codecogs.com/png.image?\dpi%7B110%7D%20\text%7BExp-Mean3%7D(a,b)=k%5E%7B\log_k(\sqrt%5Bb%5D%7Ba%7D)*\log_k(\sqrt%5Ba%5D%7Bb%7D))
.
If and b are real, then![[Image: png.image?\dpi%7B110%7D%20\text%7BExp-Mean3%7D(a..._k(b)%7D%7Ba*b]](https://latex.codecogs.com/png.image?\dpi%7B110%7D%20\text%7BExp-Mean3%7D(a,b)=k%5E\frac%7B\log_k(a)*\log_k(b)%7D%7Ba*b)
.
What about defining![[Image: png.image?\dpi%7B110%7D%20\text%7BExp-Mean4%7D(a,b)]](https://latex.codecogs.com/png.image?\dpi%7B110%7D%20\text%7BExp-Mean4%7D(a,b))
as ![[Image: png.image?\dpi%7B110%7D%20\text%7Bsexp%7D(\frac%7B...log%7D(b)%7D2)]](https://latex.codecogs.com/png.image?\dpi%7B110%7D%20\text%7Bsexp%7D(\frac%7B\text%7Bslog%7D(a)+\text%7Bslog%7D(b)%7D2))
, for some base such as the Tetra-Euler Number?
What if you defined an exponential mean as a mean such that
Then
If a and are complex, then
If and b are real, then
What about defining
Please remember to stay hydrated.
ฅ(ﾐ⚈ ﻌ ⚈ﾐ)ฅ Sincerely: Catullus /ᐠ_ ꞈ _ᐟ\
ฅ(ﾐ⚈ ﻌ ⚈ﾐ)ฅ Sincerely: Catullus /ᐠ_ ꞈ _ᐟ\