Solve for x the equation 5(8e^2x - 3)^3 = 625?
2 Answers
justaguide | College Teacher | (Level 2) Distinguished Educator
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.
giorgiana1976 | College Teacher | (Level 3) Valedictorian
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.