r=a/b is positive rational number, (a,b)=1, b>0. k1,k2,…,kn are distinct odd rational primes. Further, (a,ki)=(b,ki)=1. Is that logr,log(k1),log(k2),…,log(kn) are linearly independent?

If the condition b>0 is removed, will they be linearly dependent?