Solve: \(\sqrt{\frac{a}{b}} = \left(\frac{b}{a}\right)^{1-2x}\)
Solution
\[ \sqrt{\frac{a}{b}} = \left(\frac{b}{a}\right)^{1-2x} \]
\[ \Rightarrow \left(\frac{a}{b}\right)^{1/2} = \left(\frac{a}{b}\right)^{-(1-2x)} \]
\[ \Rightarrow \left(\frac{a}{b}\right)^{1/2} = \left(\frac{a}{b}\right)^{2x-1} \]
\[ \Rightarrow \frac{1}{2} = 2x – 1 \]
\[ \Rightarrow 2x = \frac{3}{2} \]
\[ \Rightarrow x = \frac{3}{4} \]
Final Answer:
\[ \boxed{x = \frac{3}{4}} \]