I have a question regarding Absolute Extrema.

f(x) = 7xlnx

Find the absolute extrema. For the answer, my professor got 1/e. I do not understand the last step of this. He had lnx = -1 and then he turned it into

e^lnx = e^-1, which followed x = e^-1. Is there any link with x and e ^lnx I am missing?

Thanks