If `a > 1, b > 1,` then the minimum value of `log_b a + log_a b` is

If agt1,bgt1,cgt1,dgt1 then the minimum value of log_(b)a+log_(a)b+log_(d)c+log_(c)d , is

If a,b,c,d in R^(+)-{1} , then the minimum value of log_(d) a+ log_(c)b+log _(a)c+log_(b)d is

If a,b,c,d in R^(+)-{1} , then the minimum value of log_(d) a+ log_(c)b+log _(a)c+log_(b)d is

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

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

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

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

If a,b in(0,1) ,then minimum value of log_(a)(ab)-log_(b)((b)/(a)) is

If a,b,c are non-zero and different from 1, then the value of |{:( log _(a) 1 , log _(a) b , log _(a) c ), ( log _(a ) ((1)/(b)), log _(b) 1 ,log_(a) ((1)/(c))), ( log _(a) ((1)/(c)) ,log _(a)c, log _(c) 1):}| is

If a^4b^5=1 then the value of log_a(a^5b^4) equals