Find the equation of the tangent line to the curve y = e^2 when it is parallel to 2x - y = 7

Question

i need help on this question, what are the steps?

Answer 1

The line 2x - y = 7 has slope 2.

So, we need to find x so that (e^x)' = 2

e^x = 2

x = ln2

Point of tangency is (ln2, e^ln2) = (ln2, 2)

Equation of tangent line: y - 2 = 2(x - ln2)

So, y = 2x - 2ln2 + 2