Is this the only irrational or transcendental number that works.
What about log10 instead of ln

On Tue, 5 Sep 2023 11:23:04 -0700 (PDT), Dan joyce
<danj4084@gmail.com> wrote:

>Is this the only irrational or transcendental number that works.
>What about log10 instead of ln

Is there some contest where you try to make trivial formulas as
complicated as possible.

1 / (e^-e) = e^e

e^e / e^2 = e^(e-2)

ln e^x = x by definition so ln e^(e-2) = e-2

You can substitute any real value for the '2' in both places and the
equation still holds.

You can use any value in place of e as long as you replace ln with the
log function using that value as its base.

ln is seldom written as log_e (that's as close as I can come to a
subscript) and is verbally expressed as the logarithm function using
base 'e'.

log is sometimes written log_10 to avoid confusion and is verbally
expressed as the logarithm function using base '10'.

If I remember correctly, log_2 has some usefulness.

So, to answer your question, there are other irrational and
transcendental values with similar expressions. For example

log_pi(((1/(pi^-pi)))/pi^2)=pi-2

And while I don't know of anyone ever producing a table of log_pi
values, it is trivial to compute log_pi(x) for any real x using only
ln or log.

--
Remove del for email