Is this identity correct?

Question

Is this identity true? Wolfram|Alpha thinks is not.

$$x^{ln(x^3)} = e^{3\,[ln(x)]^2}$$

That's how I demonstrated it:

$${\left(e^{ln(x)}\right)}^{3\,ln(x)} = e^{3\,[ln(x)]^2}$$

$$e^{3\,ln(x)\,ln(x)} = e^{3\,[ln(x)]^2}$$

$$e^{3\,[ln(x)]^2} = e^{3\,[ln(x)]^2}$$

Answer 1

taking the logarithm of both sides we obtain $\ln(x^3)\ln(x)=3\ln(x)^2$ and the right hand side is $3\ln(x)^2\ln(e)=3\ln(x)^2$ thus the equation $x^{\ln(x^3)}=e^{3\ln(x)^2}$ is true for $x>0$.