" The natural number n for which the expression "y=5(log_(3)n)^(2)-log_(3)n^(12)+9" ,has the minimum value is "

Find the value of the expression 5^(log_(sqrt(5))2)+9^(log_(3)7)-8^(log_(2)5)

If a_(n)>1 for all n in N then log_(a_(2))a_(1)+log_(a_(3))a_(2)+....log_(a_(1))a_(n) has the minimum value of

If a_n>1 for all n in N then log_(a_2) a_1+log_(a_3) a_2+.....log_(a_1)a_n has the minimum value of

If a_ngt1 for all ninN ,then log_(a_2)a_1+log_(a3)a_2+.....+log_(an)a_(n-1)+log_(a1)a_n has the minimum value

N=log_(2)5*log_((1)/(6))2*log_(3)((1)/(6)) then 3^(N) is

If [.] denotes the greatest integer function,then thevalue of natural number n satisfying the equation [log_(2)1]+[log_(2)2]+[log_(2)3]+......+[log_(2)n]=1538, is

If x_(n)gt1 for all n in N , then the minimum value of the expression log_(x_(2))x_(1)+log_(x_(3))x_(2)+...+log_(x_(n))x_(n-1)+log_(x_(1))x_(n) is