Which of the following numbers are positive/negative : `(i) log_(sqrt(3))sqrt(2)` `(ii)log_3(4)`

Explanation

(i) Let ` log_(2)7=xrArr7=2^(x) rArrx gt 0`
(ii)Let ` log_(0.2)3= x rArr 3 = 0.2^(x) rArr x lt 0`
(iii) Let ` log_(1//3)(1//5)=x rArr 1//5 = (1//3)^(x) rArr 5 = 3^(x) rArr x gt 0`
(iv) Let ` log_(4) 3 = x rArr 3 = 4^(x) rArr x lt 0`
(v) Let ` log_(2) (log_(2)9) = x rArr log_(2) 9 = 2^(x) rArr 9 =2^(2^(x)) rArr x gt 0`