Question

Find the necessary and suppicient condition for aº - blog(a) for any complex numbers a,b.

Answer 1

ction, ie Complen er logaritha logarithm is defined as an inverse to complex exponential fue to say A lo q withm of a non-zero complex number 'a', is any complex number a such that explorea ORI 0 BAD 4 = loga if exp ca = - where ca and a are complex numbers let us ifiu R as aittilan exproifiuz) = aitiaz 4 Buichua is exp (ws : 9 us Loglal diting expcu) - Talou Since 30 a l Togas - Long lai tiang dan lain Cal To it is function a multivalue foecause of 299 (9)

oba eblogheb Logiaiila argia S e abrelelogiale 16 Bak for kez 3 - we will have Depending Debonding upon b, we have either upon one, 2 finitely many or infinitely mapy value of exp (i 2x bk) set of Real set of complex se Case when belRee Subbase · bon is an integer id noo for no el 9 os 0 Z.Z.Z - Z n-times Inco 97 TT1Pp ( times for nso if b = P/ (a Rational) begeRCG abco e Clog 2) ei f * ** (K 10.) ( Exponential tokeog . ( same Palues for Pla (Logztiaak) Kekea" in this case afla will have a distinal values 8 for k=0 al finitely many. • of bo irrational, then if there are two - integer Kft' for which lanko el bo ei laad[k-k”) , [ k=ki il bu bitiba - the eibank = e (bitiba) dal izakby do Kbz then ab will have infinite number of values ob is thalytic wheneve chose Geraneh ol logarithmie – element thang na defined as lealog oca ao log out) 9.00