Logarithms
Definition of a logarithm
"log" denotes a common logarithm (base =
10), while "ln" denotes a natural logarithm (base = e).
Properties of logarithms
These properties of logarithms come in handy
for performing complex multiplication and division
operations. They are an example of something called a
transform function, whereby one type of mathematical
operation is transformed into another type of mathematical
operation that is simpler to solve. Using a table of
logarithm figures, one can multiply or divide numbers by
adding or subtracting their logarithms, respectively. then
looking up that logarithm figure in the table and seeing
what the final product or quotient is.
Slide rules work on this principle of
logarithms by performing multiplication and division through
addition and subtraction of distances on the slide.
Marks on a slide rule's scales are spaced in
a logarithmic fashion, so that a linear positioning of the
scale or cursor results in a nonlinear indication as read on
the scale(s). Adding or subtracting lengths on these
logarithmic scales results in an indication equivalent to
the product or quotient, respectively, of those lengths.
Most slide rules were also equipped with
special scales for trigonometric functions, powers, roots,
and other useful arithmetic functions. |
