If\, 1pt ( a/b )^x - 1 = ( b/a )^x - 3, then the value of x is

Answer: Option C

$$\begin{array}{rl}& \text{Given}{\left(\frac{a}{b}\right)}^{x-1}={\left(\frac{b}{a}\right)}^{x-3}\\ & \Rightarrow {\left(\frac{a}{b}\right)}^{x-1}={\left(\frac{a}{b}\right)}^{-\left(x-3\right)}={\left(\frac{a}{b}\right)}^{\left(3-x\right)}\\ & \Rightarrow x-1=3-x\\ & \Rightarrow 2x=4\\ & \Rightarrow x=2\end{array}$$