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\begin{array}{rclcl} 1.000 \cdot 1{,}025^x &=& 5.000 &\vert& :1.000 \cr 1{,}025^x &=& 5 &\vert& \ln() \cr \ln\left(1{,}025^x\right) &=& \ln(5) &\vert& \text{3. Logarithmengesetz} \cr x\cdot \ln(1{,}025) &=& \ln(5) &\vert& : \ln(1{,}025) \cr x &=& \dfrac{\ln(5)}{\ln(1{,}025)} \approx 65{,}18 \end{array}