Question

Statement-1: `"log"_(10)x lt "log"_(pi) x lt "log"_(e) x lt "log"_(2) x`
Statement-2: `x lt y rArr "log"_(a) x gt "log"_(a) y " when " 0 lt a lt 1`
A. Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is true, Statement-2 is NOT a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Answer 1

Correct Answer - B
When `x gt 1`, we have
`"log"_(x) 10 gt "log"_(x) pi gt "log"_(x) e gt "log"_(x) 2 " " [because gt pi gt e gt 2]`
`rArr (1)/("log"_(10)x) gt (1)/("log"_(pi) x) gt (1)/("log"_(e) x) gt (1)/("log"_(2)x)`
`rArr "log"_(10) x lt "log"_(pi) x lt "log"_(e) x lt "log"_(2) x`