If `a^x=b^y=c^z` and `b^2=a c ,` then show that `y=(2z x)/(z+x)`

Explanation

To solve the problem, we start with the given equations:

1. \( a^x = b^y = c^z \)
2. \( b^2 = ac \)

From the first equation, we can express \( a \), \( b \), and \( c \) in terms of a common base. Let's denote \( k = a^x = b^y = c^z \). Thus, we can write:

\[
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