Finding the intersections between \(\displaystyle{y}={e}^{{x}}\) and

Aliana Alvarez

Aliana Alvarez

Answered question

2022-04-05

Finding the intersections between y=ex and y=x+2 algebraically?

Answer & Explanation

Mey9ci0

Mey9ci0

Beginner2022-04-06Added 14 answers

Here again appears the beautiful Lambert function : rewrite
ex=x+2ex+2=e2(x+2)ey=e2y
and the solutions are given by
x1=W(1e2)2
x2=W1(1e2)2
In fact, keep in mind that any equation which can write
A+Bx+Clog(D+Ex)=0 has solutions in terms of Lambert function.
The Wikipedia page gives series approximations.
There is no other closed form to this equation. If you cannot use it, just numerical methods will provide the solutions.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?