Question

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

Answer 1

You have an equation where both sides share a common factor: `e^(2x)`.

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^(2x)`, as follows:

`(x*cancel(e^(2x)))/cancel(e^(2x)) = (5*cancel(e^(2x)))/cancel(e^(2x))`

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

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

`x = (5*cancel(e^(2x)))/cancel(e^(2x))`

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