what is the solution of the equation 4(3-x)^4/3-5=59
Answer:
Given the equation: \(4(3-x)^{\frac{4}{3}} -5 = 59\)
Add 5 to both sides we have;
\(4(3-x)^{\frac{4}{3}} = 64\)
Divide by 4 both sides we have;
\((3-x)^{\frac{4}{3}} =16\)
or
\(3-x = (16)^{\frac{3}{4}\)
Using exponent rules;
\(a^{\frac{n}{m}} = (\sqrt[m]{a})^n\)
then;
\(3-x =( \sqrt[4]{16})^3\)
Simplify:
\(3-x = (2)^3\)
or
\(3-x = 8\)
subtract 3 from both sides we have;
\(-x = 5\)
Divide both sides by -1 we get
\(x = -5\)
Therefore, the solution for the given equation is, -5