Please help me solve this!!!!
4*(3-x)^4/3 - 5 = 59
(4/3 is an exponent)
I got to this far... (3-x)^4/3 = 16
But how do I get rid of the exponent? Please help me my final is tomorrow and I still don't know :(
(3-x)^4/3 = 16 , great so far
raise both sides to the 3/4
[(3-x)^4/3]^(3/4) = 16^(3/4)
3-x = 8
x = -5
To get rid of the exponent, you can raise both sides of the equation to the reciprocal of the exponent. In this case, the reciprocal of 4/3 is 3/4.
So, you can raise both sides of the equation (3-x)^(4/3) = 16 to the power of 3/4:
[(3-x)^(4/3)]^(3/4) = 16^(3/4)
On the left side, the exponents (4/3) and (3/4) cancel out, leaving you with (3-x)^(1) or (3-x).
Therefore, you have:
3-x = 16^(3/4)
Now, you need to solve for x.
To solve the equation (3-x)^(4/3) = 16, you can eliminate the fractional exponent by raising both sides of the equation to the reciprocal of the exponent.
Step 1: Take the reciprocal of the exponent (4/3):
Reciprocal of 4/3 = 3/4
Step 2: Raise both sides of the equation to the reciprocal power:
((3-x)^(4/3))^(3/4) = 16^(3/4)
Step 3: Simplify both sides:
(3-x)^(4/3 * 3/4) = 2^3
Step 4: Simplify the exponents:
(3-x)^(1) = 2^3
Step 5: Remove the exponent on the left-hand side:
3-x = 2^3
Step 6: Simplify the right-hand side:
3-x = 8
Step 7: Isolate the variable x:
Subtract 3 from both sides:
-x = 8 - 3
-x = 5
Step 8: Solve for x:
Multiply both sides by -1 to isolate x:
x = -5
Therefore, the solution to the equation 4*(3-x)^(4/3) - 5 = 59 is x = -5.