Happy New Year Equation
1 Image
2 MathJax
\begin{eqnarray*}
w + \ln |N| &=& \ln | ap^2 H + e^{ar} | + \ln |Y| \\
w &=& \ln | ap^2 H + e^{ar} | + \ln |Y| - \ln |N| \\
w &=& \ln | ap^2 H + e^{ar} | + \ln \left| \frac{Y}{N} \right| \\
w &=& \ln \left| \left( ap^2 H + e^{ar} \right) \cdot \frac{Y}{N} \right| \\
e^{w} &=& \left( ap^2 H + e^{ar} \right) \cdot \frac{Y}{N} \\
\left( ap^2 H + e^{ar} \right) Y &=& e^{w} \cdot N \\
ap^2 H y + e^{ar}Y &=& e^{w} \cdot N \\
ap^2 H y &=& e^{w} \cdot N - e^{ar}Y \\
H ap^2 y &=& Ne^{w} - Ye^{ar} \\
Happy &=& Ne^{w} - Ye^{ar}
\end{eqnarray*}
3 source
\begin{eqnarray*} w + \ln |N| &=& \ln | ap^2 H + e^{ar} | + \ln |Y| \\ w &=& \ln | ap^2 H + e^{ar} | + \ln |Y| - \ln |N| \\ w &=& \ln | ap^2 H + e^{ar} | + \ln \left| \frac{Y}{N} \right| \\ w &=& \ln \left| \left( ap^2 H + e^{ar} \right) \cdot \frac{Y}{N} \right| \\ e^{w} &=& \left( ap^2 H + e^{ar} \right) \cdot \frac{Y}{N} \\ \left( ap^2 H + e^{ar} \right) Y &=& e^{w} \cdot N \\ ap^2 H y + e^{ar}Y &=& e^{w} \cdot N \\ ap^2 H y &=& e^{w} \cdot N - e^{ar}Y \\ H ap^2 y &=& Ne^{w} - Ye^{ar} \\ Happy &=& Ne^{w} - Ye^{ar} \end{eqnarray*}