Question

If (21.4)^a = (0.00214)^b =100, then the value of $\frac{1}{a}$ – $\frac{1}{b}$ is :

• A. Rational but not integral
• B. Prime
• C. Irrational
• D. Composite

Answer 1

Answer: (B)

Prime

Answer 2

(21.4)^a = 100 Ž 21.4 = (100)^1/a .....(i)

(0.00214)^b = 100 Ž 0.00214 = (100)^1/b

(i)/ (ii) (100)² = (100)^1/a–1/b Ž $\frac{1}{a}$ – $\frac{1}{b}$ = 2