  In this paper we develop a method to transfer density results for primitive
automatic sequences to logarithmic-density results for general automatic
sequences. As an application we show that the logarithmic densities of any
automatic sequence along squares $(n^2)_{n\geq 0}$ and primes $(p_n)_{n\geq 1}$
exist and are computable. Furthermore, we give for these subsequences a
criterion to decide whether the densities exist, in which case they are also
computable.
  In particular in the prime case these densities are all rational. We also
deduce from a recent result of the third author and Lema\'nczyk that all
subshifts generated by automatic sequences are orthogonal to any bounded
multiplicative aperiodic function.
