The data we encounter in real life often contain missing values. In sampling methods, missing value imputation is done with different methods. This article proposes novel logarithmic type imputation methods for estimating the population mean in the presence of missing data under ranked set sampling (RSS). According to the determined theoretical results, the proposed imputation methods are found to be the most efficient in comparison to popularly known imputation methods like mean imputation, Al-Omari and Bouza (2014) imputation methods, Sohail et al. (2018) imputation methods, and Bhushan and Pandey (2016) type imputation methods utilizing RSS. Apart from this, a simulation study has been accomplished utilizing artificially drawn symmetric and asymmetric populations. The outcomes are encountered to be rather satisfactory, showing improvement over all existing imputation methods.