Queries with similar information needs tend to have similar document clicks, especially in biomedical literature search engines where queries are generally short and top documents account for most of the total clicks. Motivated by this, we present a novel architecture for biomedical literature search, namely Log-Augmented DEnse Retrieval (LADER), which is a simple plug-in module that augments a dense retriever with the click logs retrieved from similar training queries. Specifically, LADER finds both similar documents and queries to the given query by a dense retriever. Then, LADER scores relevant (clicked) documents of similar queries weighted by their similarity to the input query. The final document scores by LADER are the average of (1) the document similarity scores from the dense retriever and (2) the aggregated document scores from the click logs of similar queries. Despite its simplicity, LADER achieves new state-of-the-art (SOTA) performance on TripClick, a recently released benchmark for biomedical literature retrieval. On the frequent (HEAD) queries, LADER largely outperforms the best retrieval model by 39% relative NDCG@10 (0.338 v.s. 0.243). LADER also achieves better performance on the less frequent (TORSO) queries with 11% relative NDCG@10 improvement over the previous SOTA (0.303 v.s. 0.272). On the rare (TAIL) queries where similar queries are scarce, LADER still compares favorably to the previous SOTA method (NDCG@10: 0.310 v.s. 0.295). On all queries, LADER can improve the performance of a dense retriever by 24%-37% relative NDCG@10 while not requiring additional training, and further performance improvement is expected from more logs. Our regression analysis has shown that queries that are more frequent, have higher entropy of query similarity and lower entropy of document similarity, tend to benefit more from log augmentation.