Solve for x: (you need to surround your exponent with braces if it has more than one item in it).
Let , and then you have the quadratic , and therefore
u=5 or u=2
Then x=ln 5 or x=ln 2
Do you mean "is there a harder way"? Of course, you don't have to replace , that's just the simplest thing to do. You could recognise that and then arguing that either or .
And how do I recognise that factoring? Well, I recognize as a "quadratic in " which is essentially replacing , at least in my head, by a single variable.