The natural number n for which the expression `y=5(log_3n)^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

Let n be a positive integer such that log_2 log _2 log_2 log_2 log_2 (n) lt 0 lt log_2 log_2 log_2(n) . Let l be the number of digits in the binary expansion of n. Then the minimum and the maximum possible values of l are

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

Write the following expression as log N and find their values. (iv) 2log3-3log2

The x , y , z are positive real numbers such that (log)_(2x)z=3,(log)_(5y)z=6,a n d(log)_(x y)z=2/3, then the value of (1/(2z)) is ............