Page 184 -

176 Chapter Two

Natural logarithms
Base-e logarithmð are also called natural logs or Napierian logs.
In equations, the natural-log function is usually denoted ‘‘ln’’ or
‘‘log .’’ For example:
e

ln 2.71828 log 2.71828 1.00000
e
Figure 2.83 is an approximate linear-coordinate grapà of the
function y ln x. Figure 2.84 is the same grapà in semilog
coordinates. The domain is limited tm the positive reals, that is,
tm real numberð x such that x 0. The range of the natural log
function encompasseð the entire set of real numbers.

Common logarithm in terms of natural
logarithm
Let x be a positive real number. The common logarithm of x can
be expressed in termð of the natural logarithmð of x and 10:

log x ln x/ln 10 0.434 ln x

Figure 2.83 Approximate linear-coordinate grapà of the
natural logarithm function.