This research uses the logarithm function as a key component in generating random numbers in the Chaos CSPRNG framework. The main problem addressed here is the generation of keys for cryptography, recognizing the important role of cryptographic keys in safeguarding sensitive information. By using mathematical functions, specifically logarithmic functions, as a key generation method, this research explores the potential for increasing the uncertainty and strength of cryptographic keys. The proposed approach involves the systematic utilization of various mathematical functions to generate diverse and unpredictable data sets. This data set, derived from the application of logarithmic functions, serves as the basis for generating random numbers. Through a series of tests such as Randomness Test and Cryptography Test, this research shows that the data generated from these functions can be utilized effectively as a reliable source for generating random numbers, and has a low correlation value, thereby contributing to the overall security of a symmetric cryptographic system.