Maps and navigational tools needed a huge number of calculations, including multiplications (or divisions) of numbers with several digits. In pre-computer days it was not easy to get people who could do this with a high degree of accuracy.
Logarithms changed multiplication into addition and division into subtraction. These were operations that less skilled clerks were able to perform.
This advantage has largely disappeared with the easy availability of calculators.
The exponential function is one of the more important functions in advanced mathematics, physics and economics. The logarithm function is the inverse of the exponential function and so has very many applications.
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