Exponential Equation

I haven't had any problems solving the "easier" exponential equations,
but I'm missing some important detail in solving for x in the following
equation:

e^x + 4*e^(-x) = 5

I know the two roots of the eqation are x=0 and x=ln(4).

But what is the method of finding these?

I rearrange to get: e^x = 5 - 4*e^(-x)

then take the ln of both sides to get: x = ln(5 - 4*e^(-x))

how do I proceed from here, or have I gone about things the wrong way?

Thanks.

Jordan.