I have a very long solution . . . and it may be incomplete.
Someone check it carefully . . . please!
We begin with: .
Divide  by positive .
Take logs, base 4: .
That is: . .is negative.
Multiply  by negative .
Since , then
Multiply  by positive .
Take anti-logs: .
This is an up-opening parabola with its vertex at (-2, 1).
. . Hence, it is always above the -axis.
The inequality is true for all in the domain: .