#ourworldunseen

turns into

Wow, so let’s collect similar terms on the LHS to get:

Um, this is getting kind of complicated. At this point, it’s worthwhile making the substitution e^x = y, because then we can write e^(-x) as 1/y and get:

which we can see is a quadratic equation as soon as we multiply across by y (and move terms to one side)!

Admittedly it’s a really nasty looking quadratic, but a quadratic nonetheless. So we…solve, using whatever method of solving quadratics you’d like (quadratic formula, personally), and get…oh:

Now remember that y = e^x, so then taking logs, we end up with:

(Which I hope is the answer in the back of your textbook, because it’s late.)

Hope that helped!

ourworldunseen said: I’d say black and red but I think they’re both nice

hmm, i might wait until after prom to dye my hair blue, since i dont want to accidentally ruin my hair

although my hair does need re-dying, so i need to choose a colour. i might go back to red, since i know that suits me, or maybe purple...