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 Log

 http://functions.wolfram.com/01.04.16.0038.01

 Input Form

 Log[z^a] == a Log[z] + 2 I Pi Floor[(Pi - Im[a Log[z]])/(2 Pi)]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Log", "[", SuperscriptBox["z", "a"], "]"]], "\[Equal]", RowBox[List[RowBox[List["a", " ", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", RowBox[List["a", " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]]]]]]]

 MathML Form

 log ( z a ) a log ( z ) + 2 π π - Im ( a log ( z ) ) 2 π z a a z 2 -1 a z 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", SuperscriptBox["z_", "a_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["a", " ", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", RowBox[List["a", " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2001-10-29