In this work, we study the problem of two-encoder multiterminal source coding with side information under logarithmic loss distortion measure. We establish a single-letter characterization of the rate-distortion region of this model in the discrete memoryless case. The proof of the converse relies heavily on that of Courtade-Weissman rate-distortion region of the classic two-encoder multiterminal distributed source coding without side information; and extends it to the case in which the decoder has access to a side information stream that is statistically dependent on the sources that need to be compressed. We also apply our result to the so-called Information Bottleneck Method and establish the optimal tradeoff between complexity and accuracy of the prediction in this setting.