SOLUTION: Write the function f(x)=e^(2x)+e^(x)-6 in the form of a quadratic equation by using the appropriate substitution, and solve for x. I did not know how to do this problem, my teac

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Write the function f(x)=e^(2x)+e^(x)-6 in the form of a quadratic equation by using the appropriate substitution, and solve for x. I did not know how to do this problem, my teac      Log On


   

Question 308168: Write the function f(x)=e^(2x)+e^(x)-6 in the form of a quadratic equation by using the appropriate substitution, and solve for x.
I did not know how to do this problem, my teacher did not explain it well enough to me.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
factoring ___ f(x) = (e^x + 3) (e^x - 2)

setting f(x) to zero to find roots ___ 0 = (e^x + 3) (e^x - 2)

e^x + 3 = 0 ___ e^x = -3 negative value is not realistic

e^x - 2 = 0 ___ e^x = 2 ___ x = ln(2)