50. The value of `log_P(log_P(((P^(1/p))^(1/p))^(1/p)^(...n times))`

The expression, log_p log_p ((((p)^(1/p))^(1/p))^(1/p))....n time )^(1/p) where p > 2, p in N, when simplified is

The expression log_p.log_p(((p)^(1/p))^(1/p)........n time)^(1/p) where p>= 2 , when simplified is (A)independent of p, but dependent on n (B) independent of n, but dependent on p (C) dependent on both p & n (D) negative

The value of p satisfying log_(4)(3p-2)=log_((1)/(4))p is

The value of lim_(n to oo) (1^(p)+2^(p)+3^(p)+…+n^(p))/(n^(p+1)) is -

If p is a prime, then sum of log_(p)p^(1//2)-log_(p)p^(1//3)+log_(p)p^(1//4)-……=

If p is a prime, then sum of log_(p)p^(1//2)-log_(p)p^(1//3)+log_(p)p^(1//4)-……=

If p>1 and q>1 are such that log(p+q)=log p+log q ,then the value of log(p-1)+log(q-1) is equal to (a)0(b)1 (c) 2(d) none of these

The value of N satisfying log_(a)[1+log_(b){1+log_(c)(1+log_(p)N)}]=0 is

The value of N satisfying log_(a)[1+log_(b){1+log_(c)(1+log_(p)N)}]=0 is