When does $(x^x)^x=x^{(x^x)}$ in Real numbers? I have tried to solve this equation:$(x^x)^x=x^{(x^x)}$ in real numbers I  
got only $x=1,x=-1,x=2$ , are there others solutions ?
Note: $x$ is real number .
Thank you for your help .

Hint:
for $x>1$
$$x^{x^2} = x^{x^x}$$
$$x^2=x^x$$
$$2\log x=x\log x$$
$$x=2$$
