Question #c0954

1 Answer
Feb 12, 2018

x=e^2

Explanation:

In general, an equation with an x in a log and an x outside (or an exponential and outside the exponential such as xe^x = 1) are called transcendental equations and do not have exact / analytical solutions.

This one is a bit different. Looking at it, we may have the intuition that x = e^y. If we plug this in, the above equation becomes
e^y y^2 = 4e^2 which clearly is solved by y = 2 or x = e^2.