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Math Help - Expo-equation

  1. #1
    Super Member dhiab's Avatar
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    Exclamation Expo-equation

    Solve in R :
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  2. #2
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    Helli, dhiab!

    Solve in R: . e^{2x+1} - e^{2x+3} - e^5 \:=\:0

    Divide by e\!:\quad 2^{2x} - 2^{2x+2} - e^4 \;=\;0

    Factor: . e^{2x}(1 - e^2) -e^4 \:=\:0 \quad\Rightarrow\quad e^{2x}(1-e^2) \:=\:e^4

    Hence: . e^{2x} \:=\:\frac{e^4}{1-e^2} \quad\Rightarrow\quad (e^x)^2 \;=\;\frac{e^4}{1-e^2} \quad\Rightarrow\quad e^x \;=\;\pm\frac{e^2}{\sqrt{1-e^2}}


    But 1 - e^2 is negative . . . There are no real roots.

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