You are asking about \(\displaystyle e^x= 50x\). Rewrite it as \(\displaystyle xe^{-x}= \frac{1}{50}\). Let y= -x. Then x= -y and the equation becomes \(\displaystyle -ye^y= \frac{1}{50}\) or \(\displaystyle ye^y= -\frac{1}{50}\). Now apply the *Lambert W function* (which is defined as the inverse function to \(\displaystyle f(x)= xe^x\)) to both sides: \(\displaystyle y= W\left(-\frac{1}{50}\right)\) so \(\displaystyle x= -W\left(-\frac{1}{50}\right)\).