If , solve for t.
This is my work.
I'm stuck trying to simplify . Help?
No, your method was making things more complicated rather than simplifying. One thing that might make the solution easier to understand is to let [tex]y= e^t[tex] to start with. Since , your equation becomes . Multiply both sides by 2y to get [tex]2xy= 2y^2+ 1[tex] or . Use the quadratic formula to solve that for y and then take t= ln(y).