Problem: Solve 6e

^{-x}- e

^{x}= 1

So I did this:

ln(6e

^{-x}) - ln(e

^{x}) = ln(1)

ln(6) + ln(e

^{-x}) - ln(e

^{x}) = ln(1)

ln(6) - x - x = 0

2x = ln(6)

x = ln(6) / 2

But when I plug that answer into my calculator, it comes up 0, not 1. I'm missing something and I've been beating my head against the wall which isn't helping. It may come to me in the middle of the night but I doubt it; exponential functions was the point in my summer pre-calculus class where I got overwhelmed with the pace of the summer session, and it's coming back to haunt me now.

Thanks for any direction.