Calculating Logarithms by Hand - wikipedia

One of the main historical motivations of introducing logarithms is the formula $log_b ⁡ ( x y ) = log_b ⁡ x + log_b ⁡ y $

First known modern origin is from Napier around 1614. Napier worked decades before calculus was invented, the exponential function was understood, or coordinate geometry was developed by Descartes. But predecessor function sharing similarities dates from -2000 (quarter square multiplication), around 800 and 1544 (binary log)

see also

• The Lost Art of Logarithms / HN

Logarithmic scale

Slide rules

Starting from 2 on the lower scale, add the distance to 3 on the upper scale to reach the product 6. The slide rule works because it is marked such that the distance from 1 to x is proportional to the logarithm of x.