2e^2x-e^x=0 solve the equation

Question

I've got a test tomorrow and the only question left I can't wrap my head around is this one, all help is greatly appreciated. (This is a derived function set to zero by the way, looking for maximum value)

Answer 1

Adam, try this:

Solve by factoring out e^x.

e^x(2e^x -1)=0

So e^x=0 or 2e^x-1=0

The first can never equal zero. But for the 2nd e^x = 1/2. Take the natural log of both sides to isolate x. You will see that ln (.5) is the solution.