Solving the Logarithmic Equation: \ln(x)^{\ln(x)} = x^\ln(\ln(x))?

[Yegor]

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]

What do you get if you take x < 1? However, if x > 1, then yes, if you take ln from both sides, they are equal. In fact, when I graph it, I get a horizontal line starting from (1,0) and going to the right. I used GCalc to graph it. You can do the same in case it is just a problem with whatever graphing tool you're using.

 

[Maxos]

To give this expression (\ln(x)^{\ln(x)} = x^\ln(\ln(x))) a meaning, x must be >1, then the statement is true.
And you'll have no problems in plotting it, in fact the software you used was not interested in showing you the logic puzzles it was involved in, thus tricking you.