`N=log_2 5*log_(1/6)2*log_3 (1/6),t h e n3^N` is equal to

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

If x=(log)_k b=(log)_b c=1/2(log)_c d ,t h e n(log)_k d is equal to 6x b. (x^3)/2 c. 2x^3 d. 2x^8

Let n=2006!. Then 1/(log_(2)n)+1/(log_(3)n)+…+1/(log_(2006)n) is equal to :

Match the column Column I, Column II If x=3,t h e n(log)_4(2(log)_3(1+(log)_2(1+3Log_3x))) is equal to, p. 3 If x=100 , then 3^((log)_3logsqrt(x))-logx+log^2x is equal to, q. 1 If one of the root of the equation 2((log)_xsqrt(5))^2-3(log)_x(a)+1=0 is sqrt(5) , then the other root is, r. 1/2 If (log)_2(4. 3^x-6)-(log)_2(9^x-6)=1, then x is equal to, s. 5

lim_(n->oo)[log_(n-1)(n)log_n(n+1)*log_(n+1)(n+2).....log_(n^k-1) (n^k)] is equal to :

If sum_(r=0)^(n-1)log_(2)((r+2)/(r+1)) =prod_(r=10)^(99)log_(r) (r+1), then 'n' is equal to (A) 4 (B) 3 (C) 5 (D) 6

If a_(1), a_(2), a_(3), ………, a_(n) ….. are in G.P., then the determinant Delta = |(""loga_(n)" "loga_(n + 1)" "log_(n + 2)""),(""loga_(n + 3)" "loga_(n + 4)" "log_(n + 5)""),(""loga_(n + 6)" "loga_(n + 7)" "log_(n + 8)"")| is equal to