kill(all)$

van=facebook.com/LearningCalculus$

f(f(x))=a^x;

log(a^x)/log(a);

a^(log(a^x)/log(a));

f(x):=a^(log(a^x)/log(a));

f(f(x));

fpprec:20;

bfloat(%e);

h(a):=a^a-%e;

newton(t):=bfloat(subst(t,a,a-h(a)/diff(h(a),a)))$

newton(1.7632228343518967102b0);

f(f(f(x)));

h(a):=a^a^a-%e;

newton(t):=bfloat(subst(t,a,a-h(a)/diff(h(a),a)))$

newton(1.6010751539237287793b0);