We are asked to solve the exponential equation given below:
e^5x - 5 * e^-2x = 2e
First let's apply the exponent rules:
5x - 5 - 2x = In(2e)
Solving 5x - 5 - 2x = In(2e)
3x - 5 = In(2e)
Add 5 to both sides:
3x = In(2e) + 5
Divide both sides by 3
x = In(2e) + 5
3
x = 2.23104
x = 2.231 (To the nearest thousand)
Therefore, the correct option is A, which is The solution set is 2.231 (Round to the nearest thousand).