How to solve th eequation: 140 (1+ X) ^8 = 744 ?

Answer 1

Start by dividing both sides by 140 to get (1 + x)^8 = 5.3. The solution from that point depends on whether or not you are meant to include complex solutions.

Are you dealing with real numbers only? If so, (1 + x)^8 = 5.3 equates to 1 + x = +/- 5.3^(1/8) = +/- 1.23 ==> x = -2.23 or 0.23.

However, if you are allowed to deal with complex numbers, the equation (1 + x)^8 = 5.3 has not two but eight solutions for x, because there are eight possible eight roots for 5.3 and only two of them are real. All eight eights roots of 5.3 can be expressed easily in polar form because they have radii equal to 5.3^(1/8) = 1.23, and they have angles equal to 0, pi/4, pi/2, 3*pi/4, pi, 5*pi/4, 3*pi/2, and 7*pi/4. Those angles can also be described as n*pi/8 for n = 0 to 7. You still have to subtract 1 from each of them to solve for x.

Answer 2

140 (1+ X) ^8 = 744
Divide by 140:
(1 + x)^8 = 744/140
Take the 8th root:
1 + x = (744/140)^(1/8)
Subtract 1:
x = (744/140)^(1/8) - 1
x = 0.232198.

Answer 3

You'd first divide both sides by 140.

Then you'd take the eighth root on both sides.

Then subtract 1 from both sides.