système

Bonjour;

x^y = y^x et y = pi x ==> yLn(x) = xLn(y) et y = pi x

==> pi xLn(x) = xLn(pi x) = x(Ln(pi) + Ln(x))

==> pi Ln(x) = Ln(pi) + Ln(x)

==> (pi - 1) Ln(x) = Ln(pi)

==> Ln(x) = (Ln(pi))/(pi - 1)

==> x = e^((Ln(pi))/(pi - 1)) = (e^(Ln(pi))^(1/(pi - 1)) = pi^(1/(pi - 1))

et y = pi * pi^(1/(pi - 1)) = pi^((1/(pi - 1)) + 1) = pi^((1 + pi - 1)/(pi - 1)) = pi^(pi/(pi - 1)) .