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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 130396, 3059]*) (*NotebookOutlinePosition[ 131031, 3082]*) (* CellTagsIndexPosition[ 130987, 3078]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Examples from Section 6.2 Natural Logarithms\ \>", "Section"], Cell["p. 465", "Subsection"], Cell[CellGroupData[{ Cell["Properties of Logarithms", "Subsection"], Cell[TextData[{ StyleBox["Note:", FontWeight->"Bold"], " In ", StyleBox["Mathematica", FontSlant->"Italic"], ", the natural logarithm function is denoted by ", StyleBox["Log[]", "Input"], "." }], "Text"], Cell[CellGroupData[{ Cell["3.", "Subsubsection"], Cell["a)", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\ Log[\ Sin[t]\ ]\ - \ Log[Sin[t]\/5]\ \ == \ Log[Sin[t]]\ - \((\ Log[Sin[t]]\ - \ Log[5])\)\ == \ Log[5]\)\)], "Input"], Cell[BoxData[ \(Log[5]\)], "Output"] }, Open ]], Cell["b)", "Text"], Cell[BoxData[ \(\(\ Log[\ 3 x^2\ - \ 9 x] + \ Log[\ 1/x\ ]\ \ == \ Log[3\ x\ \((x\ - \ 3)\)]\ - \ Log[x]\ == \ Log[3 \((x - 3)\)]\ + \ Log[x]\ \ - \ Log[x]\ == \ Log[3 \((x - 3)\)]\)\)], "Input"], Cell["c)", "Text"], Cell[BoxData[ \(\(1\/2\) Log[4 r^4]\ - \ Log[2]\ == \ \(1\/2\) \((Log[2\^2]\ + \ \ Log[r\^4])\)\ - \ Log[2]\ == \ \(1\/2\) \((2\ Log[2]\ + \ 4\ Log[r])\)\ - \ Log[2]\ == \ 2\ Log[r]\)], "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Derivatives of Logarithms", "Subsection"], Cell[CellGroupData[{ Cell["15. 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