Expression 14: "x" Superscript, "x" , Baseline natural log left parenthesis, "x" , right parenthesis minus "x" "x" Superscript, left parenthesis, "x" minus 1 , right parenthesis , Baseline equals 0xxlnx−xxx−1=0
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2. Substitute y=x
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Expression 16:
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Expression 17: "x" Superscript, "x" , Baseline natural log left parenthesis, "x" , right parenthesis minus "x" Superscript, "x" , Baseline equals 0xxlnx−xx=0
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3. Simplify
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Expression 19:
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Expression 20: natural log left parenthesis, "x" , right parenthesis minus 1 equals 0lnx−1=0
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4. Divide by x^x, because x can't be 0.
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Expression 22:
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Expression 23: natural log left parenthesis, "x" , right parenthesis equals 1lnx=1
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Expression 24: "x" equals "e"x=e
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Add 1 and solve.
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Expression 26:
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Expression 27: "x" equals "y" equals "e"x=y=e
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x=y, so y also equals e. This means the intersection is at (e,e)
