You’ve discussed "f(x)=f-1(x)”in one of your videos but I’ve been wrapping my head around this one: "Logx(base a)=a^x”

No Real solution. log(x) < x and a^x > x and since they are reflections in the line y = x,

y =log(x) and y = a^x will not intersect. Graph y = ln(x) and y = e^x and you will see.