If `log_p(q)+log_q(r)+log_r(p)` vanishes where p,q,r are positive reals different than unity then the value of `(log_p(q))^3+(log_q(r))^3+(log_r(p))^3`

lf log_pq+log_q r +log_r p vanishes where p, q and r are positive reals different than unity then the value of (log_p q)^3+(log_qr)^3+(log_rp)^3 is a) an odd prime b)an even prime c)an odd coposite d) an irrational number

If log_(p)q+log_(q)r+log_(r)p vanishes where p,q and r are positive reals different than unity then the value ol (log_(p)q)^(3)+(log q_(r))^(3)+(log r_(p))^(3) is a) an odd prime b)an even prime c)an odd coposite d) an irrational number

If pqr = 1 then find the value of log_(rq)p+log_(rp)q+log_(pq)r .

If p and q are positive numbers other than 1, then the least value of |log_(q)p+log_(p)q| is ______.

log_(a)((P)/(Q))=log_(a)P-log_(a)Q

Prove that : (v) p^(log_(x)q) = q^(log_(x)p)

If log_(p)x=alpha andlog _(q)x=beta, then the value of log_((p)/(q))x is

If p^(th), q^(th), r^(th) terms of a geometric progression are the positive numbers a,b,c respectively, then the angle between the vectors (log a^(2)) I + (log b^(2)) j + (log c^(2))k and (q - r) I + (r - p) j + (p - q) k is