Final answer:
The Muslim scholar who is recognized for laying the important groundwork in mathematics that eventually led to the development of logarithms is Al-Khwarizmi, not directly for logarithms but for his significant contributions in algebra.
Step-by-step explanation:
The Muslim scholar credited as the father of logarithms is Al-Khwarizmi. Although other Muslim scholars like Ibn Sina (Avicenna) and Ibn Rushd (Averroes) have made significant contributions to various fields, it is Al-Khwarizmi who is particularly known for his pioneer work in mathematics which includes the foundational text 'The Compendious Book on Calculation by Completion and Balancing'. His work in algebra was instrumental for the development of mathematical concepts, but it's important to note that the concept of logarithms as we understand them today was developed much later by John Napier. Therefore, Al-Khwarizmi is not directly responsible for logarithms; however, his work laid important groundwork for mathematical concepts that would include logarithms in the future.