If \((\frac{a}{b})^{x-1}=(\frac{b}{a})^{x-3}\), then the value of \(x\) is:
Answer: C
Given \((\frac{a}{b})^{x-1}=(\frac{b}{a})^{x-3}\)
\(\Rightarrow (\frac{a}{b})^{x-1}= (\frac{a}{b})^{-(x-3)}=(\frac{a}{b})^{(3-x)}\)
\(\Rightarrow x-1=3-x\)
\(\Rightarrow 2x=4\)
\(\Rightarrow x=2\)