> evalf[25](log(4));

                      1.386294361119890618834464

> evalf[25](1+log(9/2));

                      2.504077396776274073373258

> factor(subs(t=(1-a)/(b+1-a),b*t/(b*t+a*(1-t)^b)));

               /
  - b (-1 + a)/|
               \

                    /    b    \b       /    b    \b    2 /    b    \b
        b - b a + a |---------|  b + a |---------|  - a  |---------|
                    \b + 1 - a/        \b + 1 - a/       \b + 1 - a/

        \
        |
        /

> plot({mu,sqrt(2*mu*log(128*mu/Pi))},mu=6..13);

> evalf[25](128/Pi);

                      40.74366543152520595683425

> evalf[25](exp(1/78));

                      1.012903047932001858318551

> evalf[25](sqrt(Pi/2));

                      1.253314137315500251207882

> 
