CALCULUS HELP!!!! what point tangent to line?

Question

At what point on the curve
y = 8 + 2e^x − 3x
is the tangent line parallel to the line
3x − y = 6?

Answer 1

The line whose equation is 3x - y = 6 has a slope of 3.

The slope of the tangent line to y = 8 + 2e^x - 3x is

y' = 2e^x - 3. To be parallel to 3x - y = 6,

2e^x - 3 = 3

2e^x = 6

e^x = 3

x = ln 3

So the point on the curve is

(ln 3, 8 + 2e^ln3 - 3 ln 3)

= (ln 3, 14 - 3 ln 3)