If `ageqb >1,` then find the largest possible value of the expression `(log)_a(a/b)+(log)_b(b/a)dot`

The least value of the expression 2(log)_(10)x-(log)_x(0.01)dot for x >1 is

If log_(sqrt8) b = 3 1/3 , then find the value of b.

Prove log_(b)b = 1

If log_2(a+b)+log_2(c+d)ge4 . Then the minimum value of the expression a+b+c+d is

In triangle A B C , if /_A=pi/4, then find all possible values of tanBtanCdot

Find the value of (log)_2(2 9 3-2)+(log)_2(12 3 3+4+4 9 3)dot

If a,b,c be three such positive numbers (none of them is 1) that (log_(b)a log_(c )a-log_(a)a) + (log_(a)b log_(c )b-log_(b)b) + (log_(a)c log_(b)c-log_(c )c) = 0 , the prove that abc = 1.

The least value of the expression 2(log)_(10)x-(log)_x(0. 01),forx >1, is a. 10 b. 2 c. -0.01 d. none of these

Match the statement/expressions in Column I with the statements/expressions in Column II. Column I Column II The minimum value of (x^2+2x+4)/(x+2) is (p) 0 Let Aa n dBb e3x3 matrices of real numbers, where A is symmetric, B is skew symmetric, and (A+B)(A-B)=(A-B)(A+B) if (A B)^t=(-1)^kA B , where (A B)^t is the transpose of the matrix A B , then the possible values of k are (q) 1 Let a=(log)_3(log)_3 2. An integer k satisfying 1<2^(-k+3^((-1)))<2, must be less than (r) 2 In sintheta=cosvarphi, then the possible values of 1/pi(theta+-varphi-pi/2) are (s) 3

If a ,b ,c ,d in R^+-{1}, then the minimum value of (log)_d a+(log)_b d+(log)_a c+(log)_c b is (a) 4 (b) 2 (c) 1 (d)none of these