some useful formulae the symbols abcr and represent real numbersm and are positive integersand indices and are non-negative integers binomial formulae ( ) ab ( ) ab ( )( ba ( ) ab powers and roots - /(ar ar as ar+ as bs (ab) (ar ) ars asr (as ) / ar /as ar- as /bs ( / ) and the following are special cases of the aboven nb np ab ab / am/ am -( / / am / ) logarithms definitionthe logarithm of to base awritten as loga cis the real number satisfying the equation ab in which we assume that and there are two special cases worth notingnamely loga since and loga since from the definitionwe immediately see thataloga and loga ab and we can move easily from one base to another usingloga loga loga