Something seems fishy about this to me. But I don't know what.
Others have gotten the math right, let me just add
some terminology:
Alas ln() is not a function.
It is a mathematical relation, not a function.
This is particularly deceptive because the familiar
case of ln() restricted to positive real numbers is
a function.
The critical property of a function is that it has
a _unique_ ordinate for each abscissa.
x=y implies f(x)=f(y) _provided_ f is a function.
Looking at it the other way,
g(x)=g(y) implies x=y _provided_ g() is one-to-one.
Alas exp() is not one-to-one.
This is deceptive because the familiar case of exp()
restricted to real numbers is one-to-one.
The equivalent "proof" involving arcsin(sin()) is
easier to visualize.
This posting is the position of the writer, not that of Fischer,
Kasparov, or Capablanca.
This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.