I'm trying to solve for n in the following inequality

|4^(1/n) - 1| < x

where n is a natural number and x is a positive real number. I feel like i should be able to do this but i can't think of how. Could someone please help me out with this?

I'm also at a loss for how to solve for n with

100^n / n! < x

but I think i might be able to figure that out once i know how to work with the first one.