Question

If $a^x=b^y=c^{z}and{b}^2=ac$, then the value of $y$ is

Answer 1

Finding the value of $y$:

Given $a^x=b^y=c^{z}and{b}^2=ac$

$$\begin{gathered} Let{a}^x=b^y=c^z=k \\ Soa=k^{1/x} \\ b=k^{1/y} \\ c=k^{1/z} \\ {b}^2=ac \\ {k}^{2/y}=k^{1/x}{k}^{1/z} \\ {k}^{2/y}=k^{1/x+1/z} \\ 2/y=1/x+1/z \\ 2/y=(z+x)/xz \\ y=2xz/(z+x) \end{gathered}$$

Hence, the value of $y$ is $y=2xz/(z+x)$.