Solve for x the equation 5(8e^2x - 3)^3 = 625?

We'll divide by 5 both
sides:

5(8e^2x - 3)^3 =
625

(8e^2x - 3)^3 = 125

We'll
take cube root both sides:

8e^2x - 3 =
5

We'll add 3 both
sides:

8e^2x = 8

We'll divide
by 8:

e^2x = 1

We'll
take natural logarithms both sides:

ln e^2x = ln
1

We'll apply the power property of
logarithms:

2x ln e = ln 1

But
ln e  =1 and ln 1 = 0.

2x =
0

The solution of the equation is x =
0.