Question

Solve the exponential equation. Express irrational solutions as decimals correct to the nearest thousandth.5x -5.e-2x = 2eSelect the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The solution set is(Round to the nearest thousandth as needed. Use a comma to separate answers as needed.)OB. The solution is the empty set.

Answer 1

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).