To avoid any confusion, it would help that you provide the GSE number of the study.
When you say that you "need to do log-normalize", to which log base are you referring? Most / all array data undergoes log [base 2] (log2) transformation, in which case, this is what you have already done via:
For each GEO record for array data, there is R code retrievable via the blue Analyze with GEO2R blue button on the main accession page. This should provide code to automatically detect whether or not the data is log2 transformed and, if not, it will do this for you.