Lösung Exponentialgleichungen (Logarithmieren)

Version 7.1 von Kim Fujan am 2025/05/20 09:08

\( e^x=3 \quad \left| ln( ) \)
\( ln(e^x)=ln(3) \)
\( x=ln(3) \)
\(\mathbb{L}= \left\{ ln(3) \right\} \)
\( 2e^x-4=8 \quad \left|+4\)
\( 2e^x=12 \quad \left|:2\)
\( e^x=6 \quad \left| ln( ) \)
\( x=ln(6) \)
\(\mathbb{L}= \left\{ ln(6) \right\} \)
\( 2e^{-0.5x}=6 \quad \left|:2 \)
\( e^{-0.5x}=3 \quad \left| ln( ) \)
\( -0.5x=ln(3) \quad \left|\cdot (-2) \)
\( x=-2 \cdot ln(3) \)
\(\mathbb{L}= \left\{-2 \cdot ln(3) \right\} \)
\( e^x=-5 \quad \left| ln( ) \)
\(x=ln(-5)\)
keine Lösung!
\(\mathbb{L}= \left\{ \right\} \)
\( 4\cdot 5^x=100 \quad \left|:4 \)
\( 5^x=25 \quad \left| \text{Exponentenvergleich} \)
\( 5^x=5^2 \)
\( x=2 \)
\(\mathbb{L}= \left\{ 2 \right\} \)