Use the Henderson-Hasselbalch equation.
pH=pKa (of propanoic acid) + log(propanoate concentration/propanoic acid concentration)
=-log(1.3*10^-5) + log((5.2*10^-3)/(0.1))=3.6.
So the answer is A.
lol random equation from uni chem much?

Me too hehe yay!
Since it's not in the Chemistry study design, are we still allowed to use this equation for questions?
It's not part of VCE, don't worry.
Besides it's actually nothing special.
The Henderson-Hasselbalch equation is pH = pKa + log([base]/[acid])
where pKa = -log(Ka)
All logs are base 10
It's very easy to prove if you assume [base] and [acid] at equilibrium are their initial values, which is the requirement for using this equation.
Ka = [H+][base]/[acid]
log(Ka) = log([H+]) + log([base]/[acid])
-log([H+]) = -log(Ka) + log([base]/[acid])
pH = pKa + log([base]/[acid])
So yeah...nothing special, just a shorthand