i know how to do the majority of these type of questions, but i don't know how to simplify this one all the way..
8(2x-1)^3= 125
i know you could go
(2x-1)^3= 125/8
(2x-1)^3= (5/2)^3
but how can i simplify any further, and yes there is an answer.
nevermind i got it now
8 is the cube of 2 and 125 is the cube of 5. Therefore
[2(2x-1)]^3 = 5^3
That means that 2(2x-1) = 5
Take it from there
To simplify the equation (2x-1)^3 = (5/2)^3 further, you can take the cube root of both sides of the equation. By doing so, you'll eliminate the exponent of 3 on both sides and solve for the expression inside the parentheses, 2x-1.
Taking the cube root of both sides of the equation, you get:
∛[(2x-1)^3] = ∛[(5/2)^3]
Simplifying further, you have:
2x - 1 = 5/2
Now, you can solve for x by isolating the variable on one side of the equation. First, add 1 to both sides of the equation:
2x - 1 + 1 = 5/2 + 1
This simplifies to:
2x = 5/2 + 2/2
Which further simplifies to:
2x = 7/2
Finally, divide both sides of the equation by 2 to solve for x:
(2x)/2 = (7/2)/2
This simplifies to:
x = 7/4
So, the solution to the equation is x = 7/4.