Question

If 2^x=3^y=12^z then prove it 2/x = 1/z -1/y.​

Answer 1

`\begin{array}{l} 2^x = 3^y = 12^z \\ 2^x = 3^y = 2^(2z) \cdot 3^z \\ \Rightarrow 3 = 2^{(x)/(y)} \\ \Rightarrow 2^x = 2^(2z) \cdot 2^{(xz)/(y)} \\ \Rightarrow x = 2z + (xz)/(y) \\ \Rightarrow xy = 2zy + xz \\ \Rightarrow 2zy = xy - xz \\ \text{Dividing both sides by }xyz,\text{ we get:} \\ (2)/(x) = (1)/(z) - (1)/(y) \end{array}`