The fact that the logarithm function converts the multiplication of two
numbers to the addition of their logarithms:
log(uv) = log(u) + log(v)
was discovered by John Napier in the 1600's. This property of logarithm
was used to invent the mechanical device called the slide rule and it
allowed scientists, engineers and navigators to perform multiplication
and division much more quickly than by hand.
Slide rules were the portable calculators of their age (approximately
300 years from about 1700 to 1975).
The picture shown to the right is of the astronaut Buzz Aldrin (2nd man
to walk on the moon in 1969) using a slide rule to perform calculations
related to a spacecraft midcourse navigation correction.
The introduction of electronic calculators in the 1970's made slide rules
obsolete and students today are often not taught well the importance of
the fact that the logarithm function converts multiplication to addition.
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Below is a working slide rule from http://www.antiquark.com/sliderule/sim/n909es/virtual-n909-es.html
You can use a mouse to move the center slide as well as the clear cursor.
To compute 2.30 x 3.70 move the 1 of scale C to 2.30 of scale D, then move the clear cursor to
3.70 on scale C, the number on scale D is the product.