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

1 Answer
May 15, 2015

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!