Question

Solve (z-5)3/5 =2 where z is a real number. Simplify your answer
as much as possible

Answer 1

The simplified answer is z ≈ 7.924.

Explanation:

To solve the equation (z - 5)^(3/5) = 2, where z is a real number, we can follow these steps:

1. Raise both sides of the equation to the power of 5/3 to eliminate the fractional exponent:

[(z - 5)^(3/5)]^(5/3) = 2^(5/3)

2. Simplify the left side:

(z - 5)^(3/5 * 5/3) = 2^(5/3)

(z - 5)^1 = 2^(5/3)

3. Simplify further:

z - 5 = 2^(5/3)

4. Add 5 to both sides of the equation to isolate z:

z = 2^(5/3) + 5

Now, let's simplify the expression on the right-hand side, using an approximate decimal value for 2^(5/3):

z ≈ 2^(5/3) + 5

z ≈ 2.924 + 5

z ≈ 7.924

Therefore, the simplified answer is z ≈ 7.924.