55=60/(1+e-06x) looks a little strange, so I'll leave interpreting what e-06x is meant to be till the end.
Rewrite the equation: 1+e-06x=60/55=12/11, e-06x=12/11-1=1/11.
e06x=11.
Now, e06x could mean e6x, e0.06x, or e0.6x, so I'll provide three answers:
(1) e6x: 6x=ln(11), x=ln(11)/6=0.39965 approx.
(2) e0.06x: x=ln(11)/0.06=39.965 approx.
(3) e0.6x: x=ln(11)/0.6=3.9965 approx.