solve the eqn:
1/log(base 4) (x+1)/(x+2) < 1/log(base 4) (x+3)
I already solved this somewhere . . . Here is it again.
Note that the domain is: .
. . Hence: .
Multiply  by negative
Multiply  by positive
Take anti-logs: .
. . which simplifies to: .
This is an up-opening parabola whose vertex is at (-2,1).
. . Hence, the function is always positive.
The inequality is true for any in the domain: .