what is the solution of the equation 8=(x-3)^3/4
It's not making sense I try to solve it but I don't get 8.
below are the plug in choices.
16
13
19
11
you need to raise both sides to the 4/3 power that makes
8 raised to the 4/3 which means to find the cube root of 8 which is 2 then raise 2 to the 4th power = 16
4/3 times 3/4 = 1 so the power on x-3 is just one
16 = x-3
19 = x
Check by going back to the original problem and it does work.
thank you!
To find the solution to the equation 8 = (x - 3)^(3/4), we need to isolate the variable x.
Step 1: Raise both sides to the power of 4/3 to cancel out the exponent of 3/4:
(8)^(4/3) = [(x - 3)^(3/4)]^(4/3)
Simplifying the left side:
8^(4/3) = 2^2 = 4
The right side becomes:
(x - 3)^(3/4 * 4/3) = (x - 3)^1 = (x - 3)
Step 2: Set the resulting expression equal to 4:
(x - 3) = 4
Step 3: Solve for x:
Add 3 to both sides:
x = 4 + 3 = 7
Therefore, the solution to the equation 8 = (x - 3)^(3/4) is x = 7.
Now let's check if any of the given choices (16, 13, 19, 11) satisfy the equation:
For x = 16:
8 = (16 - 3)^(3/4)
8 = 13^(3/4)
This is not true, so 16 is not the solution.
For x = 13:
8 = (13 - 3)^(3/4)
8 = 10^(3/4)
This is also not true, so 13 is not the solution.
For x = 19:
8 = (19 - 3)^(3/4)
8 = 16^(3/4)
This is still not true, so 19 is not the solution.
Finally, for x = 11:
8 = (11 - 3)^(3/4)
8 = 8^(3/4)
This is true, so x = 11 is the solution.
Thus, the correct plug-in choice is 11.