We propose incremental logarithmic time-series technique as a way to deal with time-based representations of large and dynamic event data sets in limited space. Modern data visualization problems in the domains of news analysis, network security and financial applications, require visual analysis of incremental data, which poses specific challenges that are normally not solved by static visualizations. The incremental nature of the data implies that visualizations have to necessarily change their content and still provide comprehensible representations. In particular, in this paper we deal with the need to keep an eye on recent events together with providing a context on the past and to make relevant patterns accessible at any scale. Our technique adapts to the incoming data by taking care of the rate at which data items occur and by using a decay function to let the items fade away according to their relevance. Since access to details is also important, we also provide a novel distortion magnifying lens technique which takes into account the distortions introduced by the logarithmic time scale to augment readability in selected areas of interest. We demonstrate the validity of our techniques by applying them on incremental data coming from online news streams in different time frames.