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

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We have to solve: 5(8e^2x - 3)^3 = 625 for x.

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

divide both sides by 5

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

take the cube root of both the sides

=> 8e^2x - 3 = 5

add 3 to both the sides

=> 8e^2x = 8

divide both sides by 8

=> e^2x = 1

Any number to the power 0 is 1

=> e^2x = e^0

=> 2x = 0

=> x = 0

**The solution of the equation is x = 0.**

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.**