Asked by Sara
I have the problem 2e^x = squareroot(10e^x) +3. the solution must be in exact form only.
Answers
Answered by
drwls
Let sqrt(2e^x) = y
y^2 = 2 e^x
sqrt(10e^x) = sqrt5*sqrt(2e^x)
= sqrt5*y
y^2 - sqrt5*y -3 = 0, a quadratic
B^2 - 4AC = 17
y = [sqrt5 +/- sqrt17]/2
Knowing y, use the natural log function to solve for x in exact closed form. It will probably look messy.
y^2 = 2 e^x
sqrt(10e^x) = sqrt5*sqrt(2e^x)
= sqrt5*y
y^2 - sqrt5*y -3 = 0, a quadratic
B^2 - 4AC = 17
y = [sqrt5 +/- sqrt17]/2
Knowing y, use the natural log function to solve for x in exact closed form. It will probably look messy.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.