nice problem to get my day started...I also realized that if you iscolate 1 of the x's you can end up with 50^50/x which turns it into an infinite power tower >>> x = 50^50/50^50/50^50/50^50/50... and anything divided by itself is 1 so you get 50^1^1^1^1^1..... therefore x = 50
if you're looking for any solutions other than the "by inspection" one, the fashionable tool for the job is lambert's w function. 50^(x/50) = x e^(x* ln50/50)= x 1 = x* e^(x* -ln50/50) -ln50/50 = [-ln50/50*x]*e^[-ln50/50 *x] W(-ln50/50)=-ln50/50*x x= W[-ln50/50]/[-ln50/50]
