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 Log

 http://functions.wolfram.com/01.04.16.0171.01

 Input Form

 a Log[x] + b ArcSech[y] == I Pi (1 - (-1)^(Floor[-(Arg[(Sqrt[1/y - 1] Sqrt[1 + 1/y] + 1/y)^b x^a + 1]/ (2 Pi))] - Floor[-(Arg[x^a (Sqrt[1/y - 1] Sqrt[1 + 1/y] + 1/y)^b]/ (2 Pi))])) + (-1)^(-Floor[-(Arg[x^a (Sqrt[1/y - 1] Sqrt[1 + 1/y] + 1/y)^b - 1]/ (2 Pi))] + Floor[-(Arg[(Sqrt[1/y - 1] Sqrt[1 + 1/y] + 1/y)^b x^a + 1]/(2 Pi))] + Floor[-(Arg[x^a (Sqrt[1/y - 1] Sqrt[1 + 1/y] + 1/y)^b]/Pi)] + Floor[Arg[x^a (Sqrt[1/y - 1] Sqrt[1 + 1/y] + 1/y)^b]/Pi - (2 Arg[x^a (Sqrt[1/y - 1] Sqrt[1 + 1/y] + 1/y)^b - 1])/Pi]) ArcSech[(2 x^a (Sqrt[1/y - 1] Sqrt[1 + 1/y] + 1/y)^b)/ ((Sqrt[1/y - 1] Sqrt[1 + 1/y] + 1/y)^(2 b) x^(2 a) + 1)] - 2 I Pi (Floor[(-Arg[x^a] - Arg[(Sqrt[1/y - 1] Sqrt[1 + 1/y] + 1/y)^b] + Pi)/ (2 Pi)] + Floor[(Pi - Im[a Log[x]])/(2 Pi)] + Floor[(Pi - Im[b Log[Sqrt[1/y - 1] Sqrt[1 + 1/y] + 1/y]])/(2 Pi)])

 Standard Form

 Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List[RowBox[List["a", " ", RowBox[List["Log", "[", "x", "]"]]]], "+", RowBox[List["b", " ", RowBox[List["ArcSech", "[", "y", "]"]]]]]], "\[Equal]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["Floor", "[", RowBox[List["-", FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "y"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "y"]]]]]], "+", FractionBox["1", "y"]]], ")"]], "b"], " ", SuperscriptBox["x", "a"]]], "+", "1"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]]]], "]"]], "-", RowBox[List["Floor", "[", RowBox[List["-", FractionBox[RowBox[List["Arg", "[", RowBox[List[SuperscriptBox["x", "a"], " ", SuperscriptBox[RowBox[List["(", 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RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["-", RowBox[List["Arg", "[", SuperscriptBox["x", "a"], "]"]]]], "-", RowBox[List["Arg", "[", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "y"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "y"]]]]]], "+", FractionBox["1", "y"]]], ")"]], "b"], "]"]], "+", "\[Pi]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", RowBox[List["a", " ", RowBox[List["Log", "[", "x", "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", RowBox[List["b", " ", RowBox[List["Log", "[", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "y"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "y"]]]]]], "+", FractionBox["1", "y"]]], "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], ")"]]]]]]]]]]]]

 MathML Form

 a log ( x ) + b sech - 1 ( y ) π ( 1 - ( - 1 ) - arg ( ( 1 y - 1 1 + 1 y + 1 y ) b x a + 1 ) 2 π - - arg ( x a ( 1 y - 1 1 + 1 y + 1 y ) b ) 2 π ) + ( - 1 ) arg ( x a ( 1 y - 1 1 + 1 y + 1 y ) b ) π - 2 arg ( x a ( 1 y - 1 1 + 1 y + 1 y ) b - 1 ) π + - arg ( x a ( 1 y - 1 1 + 1 y + 1 y ) b ) π - - arg ( x a ( 1 y - 1 1 + 1 y + 1 y ) b - 1 ) 2 π + - arg ( ( 1 y - 1 1 + 1 y + 1 y ) b x a + 1 ) 2 π sech - 1 ( 2 x a ( 1 y - 1 1 + 1 y + 1 y ) b ( 1 y - 1 1 + 1 y + 1 y ) 2 b x 2 a + 1 ) - 2 π ( - arg ( x a ) - arg ( ( 1 y - 1 1 + 1 y + 1 y ) b ) + π 2 π + π - Im ( a log ( x ) ) 2 π + π - Im ( b log ( 1 y - 1 1 + 1 y + 1 y ) ) 2 π ) a x b y 1 -1 -1 -1 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 b x a 1 2 -1 -1 -1 x a 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 b 2 -1 -1 x a 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 b -1 -1 2 x a 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 b -1 -1 -1 x a 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 b -1 -1 -1 x a 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 b -1 2 -1 -1 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 b x a 1 2 -1 2 x a 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 b 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 2 b x 2 a 1 -1 -1 2 -1 x a -1 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 b 2 -1 -1 a x 2 -1 -1 b 1 y -1 -1 1 2 1 1 y -1 1 2 1 y -1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["a_", " ", RowBox[List["Log", "[", "x_", "]"]]]], "+", RowBox[List["b_", " ", RowBox[List["ArcSech", "[", "y_", "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["Floor", "[", RowBox[List["-", FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "y"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "y"]]]]]], "+", FractionBox["1", "y"]]], ")"]], "b"], " ", SuperscriptBox["x", "a"]]], "+", "1"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]]]], "]"]], "-", RowBox[List["Floor", "[", RowBox[List["-", FractionBox[RowBox[List["Arg", "[", RowBox[List[SuperscriptBox["x", "a"], " ", SuperscriptBox[RowBox[List["(", 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02