If `agt1; if log_a (x_2)gt x_1` then `x_2gta^(x_1)`and If `0ltalt1` ; if `log_a (x_2)gt (x_1)` then `0lt(x_2)lt a^(x_1)`

(log x)^(log x),x gt1

Solve log_(2).(x-1)/(x-2) gt 0 .

If log_(1//8)(log_(4)(x^(2)-5))gt0 , then ______.

Solve log_(2)|x-1| lt 1 .

Find x if log_(2) log_(1//2) log_(3) x gt 0

Solve for x:log_(1//sqrt2),(x-1)gt2

Statement - 1 : If x gt 1 then log_(10)x lt log_(3)x lt log_(e )x lt log_(2)x . Statement - 2 : If 0 lt x lt 1 , then log_(x)a gt log_(x)b implies a lt b .

Solve log_(x+3)(x^(2)-x) lt 1 .

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