If the probability measures $P$ and $Q$ are mutually absolutely continuous, Kullback divergence $K(P,Q)=\int \log\left(\frac{\mathrm{d}P}{\mathrm{d}Q}\right)\mathrm{d}P$, and chi-square divergence $ \chi^2(Q,P) = \int \left( \frac{\mathrm{d}Q}{\mathrm{d}P}−1\right)^2 \mathrm{d}P$, how to prove that
$$ K(P,Q) \leqslant \frac{1}{2}\chi^2(Q,P)$$