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 f(x)= [sin^2x] (where [.] denotes the greatest integer function ) then :

int_(3)^(10)[log[x]]dx is equal to (where [.] represents the greatest integer function)

f:(2,3)->(0,1) defined by f(x)=x-[x] ,where [dot] represents 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

Evaluate lim_(xto2^(+)) ([x-2])/(log(x-2)), where [.] represents the greatest integer function.

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

Identify the following functions: f(x)=cos["x"]+[(sinx)/2] where [dot] denotes the greatest integer function.

If log_4 (x^2+x)-log_4(x+1)=2 , then the value of x is

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