$2\wedge 3\wedge 4$ could be $(2^3)^4$ or $2^{(3^4)}$. Does it make any difference? For both definitions, which is bigger: $r\wedge r\wedge r\wedge r\dots$ where the powers of $r$ go on for ever, or $(r^r)^r$, where $r$ is $\sqrt{2}$?

Power Quady

Age 16 to 18 Challenge Level:

Find all real solutions of the equation
$$(x^2-7x+11)^{(x^2-11x+30)} = 1.$$