or The graphbelowshowsthe two basicshapes:
LogarithmicFunctions
Recallfrom your previouscoursesin algebrathat a logarithmis an exponent.If the base and
then for any valueof the logarithmto the base of the valueof is denotedby
This is equivalentto the exponentialform
For example,the followingtable showsthe logarithmicformsin the first row and the correspondingexponential
formsin the secondrow.
LogarithmicForm
ExponentialFormHistorically, logarithmswith baseof werevery popular. Theyare calledthe commonlogarithms.Recently
the base has beengainingpopularitydue to its considerablerole in the field of computerscienceand the
associatedbinarynumbersystem.However, the most widelyused base in applicationsis the naturallogarithm,
whichhas an irrationalbasedenotedby in honorof the famousmathematicianLeonhardEuler. This irra-
tionalconstantis Formally, it is definedas the limit of as approacheszero.
That is,