If `(21. 4)^a=(0. 00214)^b=100`, then the value of `1/a-1/b`is0 (b) 1 (c) 2(d) 4

If `(21. 4)^a=(0. 00214)^b=100`, then the value of `1/a-1/b`is0 (b) 1

1.	If `(21. 4)^a=(0. 00214)^b=100`, then the value of `1/a-1/b`is0 (b) 1 (c) 2(d) 4
Answer» Correct Answer - C `(21.4)^(a) = 100` ` rArr a log(21.4) = 2` ` :. Log(21.4) = 2//a` …(i) From ` (0.00214)^(b) = 100`, we get ` b(log 0.00214)= 2` ` or b log(214.4 xx 10^(-4)) = 2` ` or b = 2/(log 21.4-4) = 2/(2/a-4) = 1/(1/a - 2) = a/(1-2a)` ` rArr 1/b = (1-2a)/a` ` rArr 1/a - 1/b = 2`