Positive integers `'a' and 'b'` satisfy the condition `log_2(log_(2^n) (log_(2^b) (2^100)))=0` Find the sum of all possible values of 'a'

If (2)^(log_(2)x^(2))-(3)^(log_(3)(x))-6=0 ,then sum of all possible values of x is

If log_(b)n=2 and log_(n)(2b)=2 , then nb=

Given aandb are positive numbers satisfying 4(log_(10)a)^(2)+((log)_(2)b)^(2)=1. Find the range of values of aandb.

The least positive integer x, which satisfies the inequality log_(log(x/2)) (x^2-10x+22) > 0 is equal to

Find the values of x satisfying the inequalities: log_(2)(x^(2)-24)>log_(2)(5x)

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 [.] represetns the greatest integer function) =

The possible value of x satisfying the equation log_(2)(x^(2)-x)log_(2)((x-1)/(x))+(log_(2)x)^(2)=4 is

If exactly one root of the equation x^(2)-2kx+k^(2)-1=0 satisfies the inequality log_(sqrt(3))(2-x)<=0 then find sum of all possible integral values of k

log_(2)a = 3, log_(3)b = 2, log_(4) c = 1 Find the value of 3a + 2b - 10c