If `(logx)/(q-r)= (logy)/(r-p)=(logz)/(p-q)` prove that `x^(q+r).y^(r+p).z^(p+q)=x^p.y^q.z^r`

If a=x y^(p-1),\ b=x y^(q-1) and c=x y^(r-1) , prove that a^(q-r)b^(r-p)\ c^(p-q)=1

If p+r=mq and (1)/(q)+(1)/(s)=(m)/(r ), then prove that : p:q=r:s .

if p: q :: r , prove that p : r = p^(2): q^(2) .

If the pth, th, rth terms of a G.P. are x, y, z respectively, prove that x^(q-r).y^(r-p) .z^(p-q) = 1 .

Factorize : p^3(q-r)^3+q^3(r-p)^3+r^3(p-q)^3

Factorize : p^3(q-r)^3+q^3(r-p)^3+r^3(p-q)^3

If p(q-r)x^(2) + q(r-p)x+ r(p-q) = 0 has equal roots, then show that p, q, r are in H.P.

If p(q-r)x^2+q(r-p)x+r(p-q)=0 has equal roots, then prove that 2/q=1/p+1/rdot

If p(q-r)x^2+q(r-p)x+r(p-q)=0 has equal roots, then prove that 2/q=1/p+1/rdot

If p^(th), q^(th) and r^(th) terms of G.P. are x,y,z respectively then write the value of x^(q-r) y^(r-p) z^(p-q).