Find values of 'x' so that `log_(absx)abs(x-1)ge0`.

If m = log 20 and n = log 25, find the value of x, so that : 2 log(x - 4) = 2m - n.

Solve log_(1-x)(x-2) ge-1 .

Let f(x) ={underset(ax, " "x lt0)(x^(2) , x ge0) . Find real values of 'a' such that f(x) is strictly monotonically increasing at x=0

Find the value of x satisfying log_a{1+log_b{1+log_c(1+log_px)}}=0 .

Show that: |log_ba+log_ab|ge2

Find the number of real values of x satisfying the equation. log_(2)(4^(x+1)+4)*log_(2)(4^(x)+1)=log_(1//sqrt(2)) sqrt((1)/(8))

Let f(x) ={underset(x^(2) +xb " " x ge1)(3-x " "0le x lt1). Find the set of values of b such that f(x) has a local minima at x=1.

If 0ltlog_(e)xltsqrt(x) for all xlt1, then find the value of lim_(xtooo) (log_(e)x)/(x).

find the value of x for which f(x) = ((2x-1)(x-1)^(2)(x-2)^(2))/((x-4)^(2))ge 0.

Statement-1 : f(x) = log_(10)(log_(1/x)x) will not be defined for any value of x. and Statement -2 : log_(1//x)x = -1, AA x gt 0, x != 1