lim(x->∞)[(2a-x)/(5a-x)]^x
=lim(x->∞)[1+ 3a/(x-5a)]^x
let
1/y = 3a/(x-5a)
x-5a = 3ay
x = 3ay + 5a
x->∞ ,y->∞
lim(x->∞)[1+ 3a/(x-5a)]^x
=lim(y->∞)[1+ 1/y]^(3ay+5a)
= e^3a = e
3a =1
a =1/3