If `x=4/9` satisfies the equation `(log)_a(x^2-x+2)>(log)_a(-x^2+2x+3),` then the sum of all possible distinct values of `[x]` is (where`[dot]` represetns the greatest integer function) ___

If alpha is an integer satisfying |alpha|lt=4-|[x]|, where x is a real number for which 2xtan^(-1)x is greater than or equal to ln(1+x^2), then the number of maximum possible values of alpha (where [.] represents the greatest integer function) is_____

Solve (log)_2(3x-2)=(log)_(1/2)x

Find x satisfying [tan^(-1)x]+[cot^(-1)x]=2, where [.] represents the greatest integer function.

Find the value of x in [1,3] where the function [x^2+1]([dot] represents the greatest integer function) is discontinuous.

Draw the graph of f(x) = [log_(e)x], e^(-2) lt x lt 10 , where [*] represents the greatest integer function.

Discuss the continuity of the function ([.] represents the greatest integer function): f(x)=[(log)_e x]

The domain of the function f(x)=log_e {sgn(9-x^2)}+sqrt([x]^3-4[x]) (where [] represents the greatest integer function is

Solve (log)_(2x)2+(log)_4 2x=-3//2.

The solution set of the equation x^(log_x(1-x)^2)=9 is

Evaluate : ("lim")_(xrarr2^+) ([x-2])/("log"(x-2)) , where [.] represents the greatest integer function.