# How do you solve xe^(2x)=5e^(2x)?

May 15, 2015

You have an equation where both sides share a common factor: ${e}^{2 x}$.

The simplest way is to eliminate such terms. You can think this in two different possible ways, but both end up doing the same for you: solving your equation to $x$.

First: you can divide both sides of the equation by ${e}^{2 x}$, as follows:

$\frac{x \cdot \cancel{{e}^{2 x}}}{\cancel{{e}^{2 x}}} = \frac{5 \cdot \cancel{{e}^{2 x}}}{\cancel{{e}^{2 x}}}$

This will leave you with the very result: $x = 5$.

Another possible way of thinking the problem is to pass the left ${e}^{2 x}$ to the right side, now dividing this side, in order to isolate $x$, as follows:

$x = \frac{5 \cdot \cancel{{e}^{2 x}}}{\cancel{{e}^{2 x}}}$

You choose which line of thought you prefer, but the different solutions will lead you to the same answer!