This paper employs logarithmic transformations to establish relations between continuous-time nonlinear partially observable risk-sensitive control problems and analogous output feedback dynamic games, The first logarithmic transformation is introduced to relate the stochastic information state to a deterministic information state, The second logarithmic transformation is applied to the risk-sensitive cost function using the Laplace-Varadhan lemma, In the small noise limit, this cost function is shown to be logarithmically equivalent to the cost function of an analogous dynamic game.