Question : If $(\frac{x}{y})^{5a-3}=(\frac{y}{x})^{17-3a}$, then what is the value of $a$?
Option 1: –7
Option 2: –5
Option 3: 0
Option 4: 3
Correct Answer: –7
Solution : Given: $(\frac{x}{y})^{5a-3}=(\frac{y}{x})^{17-3a}$ Making the same base for comparison, ⇒ $(\frac{x}{y})^{5a–3}=(\frac{x}{y})^{-(17-3a)}$ ⇒ $5a-3=-(17-3a)$ ⇒ $2a=-14$ $\therefore a=-7$ Hence, the correct answer is –7.
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