a^x = exp(x*ln(a))
= 1 + x*ln(a) + (x*ln(a))^2/2 + (x*ln(a))^3/6 + ...
=> 3^x+2^x = 2 + x*(ln(3)+ln(2)) + x^2*(ln(3)^2+ln(2)^2)/2 + x^3*(ln(3)^3+ln(2)^3)/6 + ...
= 2 + x*ln(6) + x^2*(...
=> (3^x)^2 + (2^x)^2 = 3^(2x) + 2^(2x)
= 2 + 2*x*ln(6) + 4*x^2*(ln(2)^2+ln(3)^2)/2 + 8*x^3*(ln(3)^3+ln(2)^3)/6 + ...
=> (3^(2x) + 2^(2x))/(3^x+2^x) ="
1 + (x*ln(6)+3*x^2*...)/(2+x*ln(6)+x^2*...)
~~ 1+(x*ln(6))/2" (for x"->"0)"
"raised to the power 1/x yields : "
(1+(x*ln(6))/2)^((2/(x*ln(6)))*(ln(6)/2))
= e^(ln(6)/2)
= sqrt(6)
