Wiskundeleraar

stelsel oplossen met de hand

$ \begin{array}{l} \left\{ \begin{array}{l} 90 = a \cdot 30^n \\ 190 = a \cdot 70^n \\ \end{array} \right. \\ \left\{ \begin{array}{l} a = \frac{{90}}{{30^n }} \\ a = \frac{{190}}{{70^n }} \\ \end{array} \right. \\ \frac{{90}}{{30^n }} = \frac{{190}}{{70^n }} \\ 90 \cdot 70^n = 190 \cdot 30^n \\ \log \left( {90 \cdot 70^n } \right) = \log \left( {190 \cdot 30^n } \right) \\ \log \left( {90} \right) + \log \left( {70^n } \right) = \log \left( {190} \right) + \log \left( {30^n } \right) \\ \log \left( {90} \right) + n \cdot \log \left( {70} \right) = \log \left( {190} \right) + n \cdot \log \left( {30^n } \right) \\ n \cdot \log \left( {70} \right) - n \cdot \log \left( {30} \right) = \log \left( {190} \right) - \log \left( {90} \right) \\ n \cdot \left( {\log \left( {70} \right) - \log \left( {30} \right)} \right) = \log \left( {190} \right) - \log \left( {90} \right) \\ \left\{ \begin{array}{l} n = \frac{{\log \left( {190} \right) - \log \left( {90} \right)}}{{\log \left( {70} \right) - \log \left( {30} \right)}} \approx {\rm{0}}{\rm{,882}} \\ {\rm{a = }}\frac{{90}}{{30^{{\rm{0}}{\rm{,882}}} }} \approx 4,48 \\ \end{array} \right. \\ W = 4,48 \cdot m^{0,882} \\ \end{array} $