1. ## Expo-equation

Solve in R :

2. 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.