(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 19403, 620] NotebookOptionsPosition[ 17404, 553] NotebookOutlinePosition[ 18198, 579] CellTagsIndexPosition[ 18155, 576] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Calcul de logarithmes", "Section"], Cell[CellGroupData[{ Cell["Calculer sans utiliser la calculatrice:", "Subsection"], Cell[CellGroupData[{ Cell[BoxData[{ FormBox[ RowBox[{ RowBox[{"Clear", "[", "x", "]"}], ";", RowBox[{"Clear", "[", "m", "]"}], ";", RowBox[{"Clear", "[", RowBox[{"a", ",", "b", ",", "c", ",", "d", ",", "log"}], "]"}], ";"}], TraditionalForm], "\[IndentingNewLine]", FormBox[ RowBox[{ RowBox[{"For", "[", RowBox[{ RowBox[{"i", "=", "1"}], ",", RowBox[{"i", "<", "3"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"a", "[", "i", "]"}], "=", RowBox[{"Random", "[", RowBox[{"Integer", ",", RowBox[{"{", RowBox[{"2", ",", "5"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"b", "[", "i", "]"}], "=", "0"}], ";", RowBox[{"While", "[", RowBox[{ RowBox[{ RowBox[{"b", "[", "i", "]"}], "==", "0"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"b", "[", "i", "]"}], "=", RowBox[{"Random", "[", RowBox[{"Integer", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "5"}], ",", "5"}], "}"}]}], "]"}]}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"c", "[", "i", "]"}], "=", RowBox[{"Random", "[", RowBox[{"Integer", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"d", "[", "i", "]"}], "=", RowBox[{"Random", "[", RowBox[{"Integer", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "4"}], ",", "4"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"i", ",", "\"\<) \>\"", ",", RowBox[{ SubscriptBox["log", RowBox[{"a", "[", "i", "]"}]], " ", "[", RowBox[{ RowBox[{"a", "[", "i", "]"}], "^", RowBox[{"b", "[", "i", "]"}]}], "]"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"i", "++"}]}]}], "]"}], ";"}], TraditionalForm], "\[IndentingNewLine]", FormBox[ RowBox[{ RowBox[{"For", "[", RowBox[{ RowBox[{"i", "=", "3"}], ",", RowBox[{"i", "<", "5"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"a", "[", "i", "]"}], "=", RowBox[{"Random", "[", RowBox[{"Integer", ",", RowBox[{"{", RowBox[{"2", ",", "5"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"b", "[", "i", "]"}], "=", "0"}], ";", RowBox[{"While", "[", RowBox[{ RowBox[{ RowBox[{"b", "[", "i", "]"}], "==", "0"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"b", "[", "i", "]"}], "=", RowBox[{"Random", "[", RowBox[{"Integer", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "5"}], ",", "5"}], "}"}]}], "]"}]}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"c", "[", "i", "]"}], "=", RowBox[{"Random", "[", RowBox[{"Integer", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"d", "[", "i", "]"}], "=", RowBox[{"Random", "[", RowBox[{"Integer", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "4"}], ",", "4"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"i", ",", "\"\<) \>\"", ",", RowBox[{ SubscriptBox["log", FractionBox["1", RowBox[{"a", "[", "i", "]"}]]], " ", "[", RowBox[{ RowBox[{"a", "[", "i", "]"}], "^", RowBox[{"b", "[", "i", "]"}]}], "]"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"i", "++"}]}]}], "]"}], ";"}], TraditionalForm], "\[IndentingNewLine]", FormBox[ RowBox[{ RowBox[{"For", "[", RowBox[{ RowBox[{"i", "=", "5"}], ",", RowBox[{"i", "<", "8"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"a", "[", "i", "]"}], "=", RowBox[{"Random", "[", RowBox[{"Integer", ",", RowBox[{"{", RowBox[{"2", ",", "5"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"b", "[", "i", "]"}], "=", "0"}], ";", RowBox[{"While", "[", RowBox[{ RowBox[{ RowBox[{"b", "[", "i", "]"}], "==", "0"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"b", "[", "i", "]"}], "=", RowBox[{"Random", "[", RowBox[{"Integer", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "5"}], ",", "5"}], "}"}]}], "]"}]}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"c", "[", "i", "]"}], "=", RowBox[{"Random", "[", RowBox[{"Integer", ",", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"d", "[", "i", "]"}], "=", RowBox[{"Random", "[", RowBox[{"Integer", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "4"}], ",", "4"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"i", ",", "\"\<) \>\"", ",", RowBox[{ SubscriptBox["log", RowBox[{"a", "[", "i", "]"}]], " ", "[", RowBox[{ RowBox[{"a", "[", "i", "]"}], "^", RowBox[{"(", RowBox[{ RowBox[{"b", "[", "i", "]"}], "/", RowBox[{"c", "[", "i", "]"}]}], ")"}]}], "]"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"i", "++"}]}]}], "]"}], ";"}], TraditionalForm], "\[IndentingNewLine]", FormBox[ RowBox[{ RowBox[{"For", "[", RowBox[{ RowBox[{"i", "=", "8"}], ",", RowBox[{"i", "<", "11"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"a", "[", "i", "]"}], "=", "10"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"b", "[", "i", "]"}], "=", "0"}], ";", RowBox[{"While", "[", RowBox[{ RowBox[{ RowBox[{"b", "[", "i", "]"}], "==", "0"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"b", "[", "i", "]"}], "=", RowBox[{"Random", "[", RowBox[{"Integer", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "5"}], ",", "5"}], "}"}]}], "]"}]}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"c", "[", "i", "]"}], "=", RowBox[{"Random", "[", RowBox[{"Integer", ",", RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"d", "[", "i", "]"}], "=", RowBox[{"Random", "[", RowBox[{"Integer", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "4"}], ",", "4"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"i", ",", "\"\<) \>\"", ",", RowBox[{"log", " ", "[", RowBox[{ RowBox[{"a", "[", "i", "]"}], "^", RowBox[{"b", "[", "i", "]"}]}], "]"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"i", "++"}]}]}], "]"}], ";"}], TraditionalForm]}], "Input", CellOpen->False, FontSize->13], Cell[CellGroupData[{ Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"1", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", RowBox[{ SubscriptBox["log", "5"], "(", FractionBox["1", "625"], ")"}]}], SequenceForm[1, ") ", Subscript[$CellContext`log, 5][ Rational[1, 625]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.431576035044387*^9, 3.431576037897264*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"2", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", RowBox[{ SubscriptBox["log", "3"], "(", "9", ")"}]}], SequenceForm[2, ") ", Subscript[$CellContext`log, 3][9]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.431576035044387*^9, 3.4315760378998623`*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"3", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", RowBox[{ SubscriptBox["log", FractionBox["1", "2"]], "(", "4", ")"}]}], SequenceForm[3, ") ", Subscript[$CellContext`log, Rational[1, 2]][4]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.431576035044387*^9, 3.431576037902763*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"4", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", RowBox[{ SubscriptBox["log", FractionBox["1", "5"]], "(", "3125", ")"}]}], SequenceForm[4, ") ", Subscript[$CellContext`log, Rational[1, 5]][3125]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.431576035044387*^9, 3.431576037905654*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"5", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", RowBox[{ SubscriptBox["log", "5"], "(", FractionBox["1", RowBox[{"5", " ", SqrtBox["5"]}]], ")"}]}], SequenceForm[5, ") ", Subscript[$CellContext`log, 5][Rational[1, 5] 5^Rational[-1, 2]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.431576035044387*^9, 3.4315760379086647`*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"6", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", RowBox[{ SubscriptBox["log", "2"], "(", FractionBox["1", SuperscriptBox["2", RowBox[{"2", "/", "3"}]]], ")"}]}], SequenceForm[6, ") ", Subscript[$CellContext`log, 2][2^Rational[-2, 3]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.431576035044387*^9, 3.431576037917012*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"7", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", RowBox[{ SubscriptBox["log", "5"], "(", RowBox[{"5", " ", RadicalBox["5", "3"]}], ")"}]}], SequenceForm[7, ") ", Subscript[$CellContext`log, 5][5 5^Rational[1, 3]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.431576035044387*^9, 3.431576037920126*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"8", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", RowBox[{"log", "(", FractionBox["1", "10"], ")"}]}], SequenceForm[8, ") ", $CellContext`log[ Rational[1, 10]]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.431576035044387*^9, 3.4315760379231663`*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"9", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", RowBox[{"log", "(", "1000", ")"}]}], SequenceForm[9, ") ", $CellContext`log[1000]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.431576035044387*^9, 3.4315760379261227`*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"10", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", RowBox[{"log", "(", "10000", ")"}]}], SequenceForm[10, ") ", $CellContext`log[10000]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.431576035044387*^9, 3.431576037929103*^9}}] }, Open ]] }, Open ]], Cell[BoxData[ RowBox[{"CellPrint", "[", RowBox[{"Cell", "[", RowBox[{"\"\\"", ",", "\"\\"", ",", RowBox[{"PageBreakAbove", "\[Rule]", "True"}]}], "]"}], "]"}]], "Input", CellOpen->False], Cell[CellGroupData[{ Cell["Solutions :", "Subsubsection", PageBreakAbove->True, GeneratedCell->True, CellAutoOverwrite->True, CellChangeTimes->{3.431576038014161*^9}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"For", "[", RowBox[{ RowBox[{"i", "=", "1"}], ",", RowBox[{"i", "<", "3"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", RowBox[{"i", ",", "\"\<) \>\"", ",", RowBox[{"b", "[", "i", "]"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"i", "++"}]}]}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"For", "[", RowBox[{ RowBox[{"i", "=", "3"}], ",", RowBox[{"i", "<", "5"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", RowBox[{"i", ",", "\"\<) \>\"", ",", RowBox[{"-", RowBox[{"b", "[", "i", "]"}]}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"i", "++"}]}]}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"For", "[", RowBox[{ RowBox[{"i", "=", "5"}], ",", RowBox[{"i", "<", "8"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", RowBox[{"i", ",", "\"\<) \>\"", ",", RowBox[{ RowBox[{"b", "[", "i", "]"}], "/", RowBox[{"c", "[", "i", "]"}]}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"i", "++"}]}]}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"For", "[", RowBox[{ RowBox[{"i", "=", "8"}], ",", RowBox[{"i", "<", "11"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", RowBox[{"i", ",", "\"\<) \>\"", ",", RowBox[{"b", "[", "i", "]"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"i", "++"}]}]}], "]"}], ";"}]}], "Input", CellOpen->False], Cell[CellGroupData[{ Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"1", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", RowBox[{"-", "4"}]}], SequenceForm[1, ") ", -4], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.431576035236845*^9, 3.4315760380966587`*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"2", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", "2"}], SequenceForm[2, ") ", 2], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.431576035236845*^9, 3.4315760380986*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"3", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", RowBox[{"-", "2"}]}], SequenceForm[3, ") ", -2], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.431576035236845*^9, 3.431576038101769*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"4", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", RowBox[{"-", "5"}]}], SequenceForm[4, ") ", -5], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.431576035236845*^9, 3.431576038103259*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"5", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", RowBox[{"-", FractionBox["3", "2"]}]}], SequenceForm[5, ") ", Rational[-3, 2]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.431576035236845*^9, 3.4315760381047783`*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"6", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", RowBox[{"-", FractionBox["2", "3"]}]}], SequenceForm[6, ") ", Rational[-2, 3]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.431576035236845*^9, 3.431576038130417*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"7", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", FractionBox["4", "3"]}], SequenceForm[7, ") ", Rational[4, 3]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.431576035236845*^9, 3.431576038162792*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"8", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", RowBox[{"-", "1"}]}], SequenceForm[8, ") ", -1], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.431576035236845*^9, 3.431576038196204*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"9", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", "3"}], SequenceForm[9, ") ", 3], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.431576035236845*^9, 3.43157603823002*^9}}], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ "10", "\[InvisibleSpace]", "\<\") \"\>", "\[InvisibleSpace]", "4"}], SequenceForm[10, ") ", 4], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{{3.431576035236845*^9, 3.43157603826276*^9}}] }, Open ]] }, Open ]] }, Open ]] }, Open ]] }, Open ]] }, WindowSize->{590, 672}, WindowMargins->{{378, Automatic}, {Automatic, 105}}, PrintingCopies->1, PrintingPageRange->{1, Automatic}, PrintingOptions->{"PrintCellBrackets"->False, "PrintMultipleHorizontalPages"->False, "PrintRegistrationMarks"->True, "PrintingMargins"->{{25.5, 25.}, {22.6875, 22.6875}}}, CellLabelAutoDelete->True, MacintoshSystemPageSetup -> \ "00<0004/0B`000003?T97OnPokT=E@UX0fL5N`?P0080004/0B`000000]P2:005\n\ 0000I00000000`<30?l00BL?00400@J>_@0000000000BV0801T1T000000P8000\n\ 000000000040000000000000009@DTiD", FrontEndVersion->"6.0 for Mac OS X x86 (32-bit) (May 21, 2008)", StyleDefinitions->"stylemath.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[590, 23, 40, 0, 44, "Section"], Cell[CellGroupData[{ Cell[655, 27, 61, 0, 39, "Subsection"], Cell[CellGroupData[{ Cell[741, 31, 7570, 228, 20, "Input", CellOpen->False], Cell[CellGroupData[{ Cell[8336, 263, 408, 11, 39, "Print"], Cell[8747, 276, 363, 9, 25, "Print"], Cell[9113, 287, 405, 11, 32, "Print"], Cell[9521, 300, 411, 11, 33, "Print"], Cell[9935, 313, 462, 12, 45, "Print"], Cell[10400, 327, 457, 12, 39, "Print"], Cell[10860, 341, 428, 11, 34, "Print"], Cell[11291, 354, 369, 10, 39, "Print"], Cell[11663, 366, 330, 8, 22, "Print"], Cell[11996, 376, 332, 8, 22, "Print"] }, Open ]] }, Open ]], Cell[12355, 388, 228, 5, 20, "Input", CellOpen->False], Cell[CellGroupData[{ Cell[12608, 397, 149, 4, 28, "Subsubsection", PageBreakAbove->True], Cell[CellGroupData[{ Cell[12782, 405, 1571, 44, 20, "Input", CellOpen->False], Cell[CellGroupData[{ Cell[14378, 453, 290, 7, 22, "Print"], Cell[14671, 462, 269, 7, 22, "Print"], Cell[14943, 471, 288, 7, 22, "Print"], Cell[15234, 480, 288, 7, 22, "Print"], Cell[15525, 489, 332, 9, 38, "Print"], Cell[15860, 500, 330, 9, 39, "Print"], Cell[16193, 511, 308, 8, 40, "Print"], Cell[16504, 521, 288, 7, 22, "Print"], Cell[16795, 530, 270, 7, 22, "Print"], Cell[17068, 539, 272, 7, 22, "Print"] }, Open ]] }, Open ]] }, Open ]] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)