# Question on exp

Is it right that $$\ln(x)^{\ln(x)} = x^\ln(\ln(x))$$?
If i take ln from both sides it looks ok. but when i try to plot $$\frac{\ln(x)^{\ln(x)}}{x^\ln(\ln(x))}$$ or $$\ln(x)^{\ln(x)} - x^\ln(\ln(x))$$? it doesn't gives me straight line. What is wrong?

AKG
To give this expression ($$\ln(x)^{\ln(x)} = x^\ln(\ln(x))$$) a meaning, x must be >1, then the statement is true.