Question

How do I solve e^2x=x+2

Answer 1

I believe you do the following:

e\[e^{2}x = x + 2\]
\[e ^{2}x - x = 2 => x(e^{2} - 1) = 2 => x = 2/(e^{2} - 1)\]

Answer 2

or do you mean e^(2x)...

Answer 3

This type of equation is best solved by graphing. Draw in the same coordinate both the curve y=e^(2x) and the line y=x+2 and you see how many intersections they have. Then either the values of x are clear if that was the intention of the problem maker or you can use Newton's methon to the function y=x+2-e(^2x) to get the values with vewry good starting values.