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Logarithms

Logarithms are the inverse functions of exponentials. With two exceptions, they look like tex2html_wrap_inline396 where a is the base. This means that tex2html_wrap_inline400 . In other words, the value of a logarithm (or log, for short) is the power to which the base must be raised in order to get the number you are taking the log of. For example, tex2html_wrap_inline402 since tex2html_wrap_inline404 . The two exceptions in form are the common log, which has an understood base of 10, written tex2html_wrap_inline406 , and the natural log, which has base e, and is written tex2html_wrap_inline190 . Note that tex2html_wrap_inline412 is only defined for x > 0. There is, in fact, an asymptote at x = 0 and this function will pass through the point (1,0).

Log functions have the following properties.

  1. tex2html_wrap_inline420
  2. tex2html_wrap_inline422
  3. tex2html_wrap_inline424
  4. tex2html_wrap_inline426
  5. tex2html_wrap_inline428


Vector Calculus
Wed Sep 17 14:50:13 MST 1997