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\[Equal] g[x], x]\)], "Input"], Cell[BoxData[ \({{x \[Rule] \[ExponentialE]\^50}}\)], "Output"] }, Open ]], Cell[BoxData[ \( (*It\ takes\ much\ longer\ for\ g \((x)\)\ to\ overtake\ f \((x)\)\ *) \ \)], "Input"], Cell[BoxData[ \( (*Example\ 7\ *) \)], "Input"], Cell[BoxData[ \( (*Try\ a\ small\ value\ of\ K\ in\ a\ log\ \(\(example\)\(:\)\)\ *) \ \)], "Input"], Cell[BoxData[ \(f[x_] := \ 3\ Log[x] + 6\)], "Input"], Cell[BoxData[ \(g[x_] := \ \(\(3.1\)\(\ \)\(Log[x]\)\(\ \)\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Solve[f[x] \[Equal] g[x], x]\)], "Input"], Cell[BoxData[ \({{x \[Rule] 1.1420073898156234`*^26}}\)], "Output"] }, Open ]], Cell[BoxData[ \( (*It\ takes\ a\ long\ time\ for\ g \((x)\)\ to\ overtake\ f \((x)\)*) \ \)], "Input"], Cell[BoxData[ \(\(\( (*Example\ 8*) \)\(\[IndentingNewLine]\)\( (*Try\ an\ x\ log \((x)\ \)\ runtime\ \(\(function\)\(:\)\)\ \ *) \)\)\)], "Input"], Cell[BoxData[ \(f[x_] := \ 2\ x\ Log[x]\ + \ 5 x\ + \ 3\)], "Input"], Cell[BoxData[ \( (*The\ 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