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The function *f* (*x*) = log_{10}*x* is called the common logarithmic
function.
The common log function is often written as *f* (*x*) = log *x* -- when log is
written without a base, the base is assumed to be 10. The "log" button on
most calculators means log_{10}.

*Examples*:*log*1000 = 3.*log*0.01 = - 2.*log*45 1.653 (using a calculator).

Figure %: *f* (*x*) = log *x*

The number 2.71828… occurs often in mathematics and nature. For this
reason, it is given a special name: *e*. Like *Π*, *e* is a number that
mathematicians use often, and it is an irrational
number, so it does not
repeat or terminate. *e* has been calculated to many decimal places, but it is
often rounded to *e* 2.718281828.

e^{1} | 2.71828 | ||

e^{2} | 7.38906 | ||

e^{3} | 20.0855 | ||

e^{4} | 54.5982 | ||

… |

The function *f* (*x*) = log_{e}*x* is called the natural logarithmic function.
The natural log function is often abbreviated *f* (*x*) = ln *x*--this is the way
it appears on most calculators. ln *e*^{x} = *x* and *e*^{ln x} = *x*.

*Examples*:*lne*^{4} = 4.*ln* = - 2.*ln*62 4.1271.*ln*230 5.4381.*ln*0.04 - 3.2189.

Figure %: *f* (*x*) = ln *x*

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