Question

$(a/b)^{x-1} = (b/a)^{x-3}$, then x = ? }

• A. 2
• B. 3
• C. 4
• D. 5

Hint:

$(\frac{a}{b})^m = (\frac{b}{a})^{-m}$.

Answer 1

The Correct Option is A

Step 1: Concept
Laws of Exponents.

Step 2: Analysis
Note that $(b/a) = (a/b)^{-1}$.
Rewrite the equation: $(a/b)^{x-1} = ((a/b)^{-1})^{x-3}$.

Step 3: Calculation
$(a/b)^{x-1} = (a/b)^{-(x-3)} = (a/b)^{-x+3}$.
Equating exponents: $x - 1 = -x + 3 \implies 2x = 4 \implies x = 2$.

Step 4: Conclusion
The value of x is 2. Final Answer: (A)