A Nice Math Olympiad Exponential Equation | Find the Value of x 

Never mind. I read it wrong.

Still, it seems it would be easier to start with xln(x)=ln(7+5sqrt(2))/3.

I thought the use of the cubic expansion and the simplification was super clever, not to mention really elegant, but you still had to use the w function which you could have used right at the start.