Lösung  Exponentialgleichungen rückwärts lösen

\[\begin{align*} 2 e^x-2 &= 0\\ 2 e^x &=2\quad \left|:2\\ e^x &=1 \\ x &= 0 \end{align*}\]

\[\begin{align*} e^{2x}-\square e^x &= 0 \\ e^x(\square-\square) &= 0 \left|\left| \text{ SVNP } \end{align*}\]

\[\ e^x \neq 0 ~und~ e^x-\square = 0\]

\[ x =\square \]

\[\begin{align*} e^{2x}-\square e^x+\square &= 0 \quad \left|\left|\text{ Subst.: } e^x:=\square\\ z^2-\square z + \square &= 0 \quad \left|\left|\text{ Mitternachtsformel/abc-Formel } & \end{align*}\]

\[\begin{align*} \Rightarrow z_{1,2}&=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}\\ z_{1,2}&=\frac{\square+\square}{\square} \end{align*}\]

\[\begin{align*} &\text{Resubst.: } z:= e^x\\ &e^x=\square \Rightarrow x \approx 0,693147...\\ \end{align*}\]