Given that a^x = b^y = c^z and b² = ac, then find the value of y

Correct Answer is : 2xzx+z2xz/x+zx+z2xz

Correct Answer is : 2xzx+z2xz/x+zx+z2xz

Test Index

Surds and Indices Practice Test 2

Question : 14 of 17

Marks: +1, -0

Given that

a^x = b^y = c^z

b^2 = ac

, then find the value of y

Solution:

Concept:

When powers are equal, set them equal to a common variable and compare their exponents.

Explanation:

Let

a^x = b^y = c^z = k

Then

a = k^{1/x}

b = k^{1/y}

, and

c = k^{1/z}

Given

b^2 = ac

, substitute these values:

(k^{1/y})^2 = k^{1/x} \cdot k^{1/z}

k^{2/y} = k^{1/x + 1/z}

Since the bases are equal, equate the powers:

\frac{2}{y} = \frac{1}{x} + \frac{1}{z}

Thus

\frac{2}{y} = \frac{x+z}{xz}

y = \frac{2xz}{x+z}

Answer:

y = \frac{2xz}{x+z}

, hence option A is correct.

Go to Question:

Prev Question

Next Question