hello to all science forum members,

recently i have constantly been coming up with the logarithmic power functions in log calculus, and there has been one question that seems impossible to solve but im 100% sure it could be solved without drawing a graph, can anyone help me with this?(its not homework by the way) thank you;

and also how on earth would you expand with an exponent of something like

etc.. can anyone give some solution or any idea when this kind of exponent comes out. can you even expand it when it comes to this point? is that why we have the natural logs and all that stuff?