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)`

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

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

If x gt 0 , show that, log (1+x) lt x

If x gt 0 , show that, x gt log (x^(2)+1)

If |x| lt 1, then 1/2 log ((1+x)/(1-x)) =

If x gt 0, then (x)/(1+x)-log (1+x)

If x gt 0 , prove that, x gt log (1+x) gt x/(1+x)

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 .

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 .

If x gt 0 , show that, 1+x log (x+sqrt(x^(2)+1)) gt sqrt(1+x^(2))