if ax by cz and b2 ac then y equals..., Surds and Indices, General Mathematics

Question:If` a^x = b^y = c^z` and` b^2 = ac,` then y equals :

A `(xz)/(x + z)` 
B `(xz)/(2(x - z))` 
C `(xz)/(2(z - x))` 
D `(2xz)/(x + z)`

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+ AnswerD

+ ExplanationLet` a^2 = b^y = c^z = k`

Then `a = k^(1/x), b = k^(1/y)` and `c = k^(1/z)`

`b^2 = ac => k^(2/y)`

` = k^(1/z) => k^(2/y) = k^(1/x + 1/z)`

`:. 2/y = 1/x + 1/z or 2/y`

`= (x + z)/(xz) or y = (2xz)/(x + z)`

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