What is the answer to ((x-5)^{3/4})^4=27 ?

The answer to ((x-5)^{3/4})^4=27 is x=8

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((x-5)^{3/4})^4=27

((x - 5)^{\frac{3}{4}})^{4} = 27

x = 8

Solution steps

((x - 5)^{\frac{3}{4}})^{4} = 27

Move

27

to the left side

((x - 5)^{\frac{3}{4}})^{4} - 27 = 0

Factor

((x - 5)^{\frac{3}{4}})^{4} - 27 : ((x - 5)^{\frac{3}{4}} + 2 7^{\frac{1}{4}}) ((x - 5)^{\frac{3}{4}} - 2 7^{\frac{1}{4}}) ((x - 5)^{\frac{3}{2}} + 3 \cdot 3^{\frac{1}{2}})

((x - 5)^{\frac{3}{4}} + 2 7^{\frac{1}{4}}) ((x - 5)^{\frac{3}{4}} - 2 7^{\frac{1}{4}}) ((x - 5)^{\frac{3}{2}} + 3 \cdot 3^{\frac{1}{2}}) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

(x - 5)^{\frac{3}{4}} + 2 7^{\frac{1}{4}} = 0 or (x - 5)^{\frac{3}{4}} - 2 7^{\frac{1}{4}} = 0 or (x - 5)^{\frac{3}{2}} + 3 \cdot 3^{\frac{1}{2}} = 0

Solve

(x - 5)^{\frac{3}{4}} + 2 7^{\frac{1}{4}} = 0 :

No Solution for

x \in R

Solve

(x - 5)^{\frac{3}{4}} - 2 7^{\frac{1}{4}} = 0 : x = 8

Solve

(x - 5)^{\frac{3}{2}} + 3 \cdot 3^{\frac{1}{2}} = 0 :

No Solution for

x \in R

x = 8

Verify Solutions:

x = 8

True

The solution is

x = 8

y, x = 4 - y + 9

y, x = 4 - y + 7

\frac{x}{4} = x

5 x + 1 = 10

What is the answer to ((x-5)^{3/4})^4=27 ?
The answer to ((x-5)^{3/4})^4=27 is x=8
Solve for x: ((x-5)^{3/4})^4=27
The solution is x=8