Happy New Year Equation

1. Image

2. MathJax

\begin{array}{rcl} w + \ln | N | & = & \ln | a p^{2} H + e^{a r} | + \ln | Y | \\ w & = & \ln | a p^{2} H + e^{a r} | + \ln | Y | - \ln | N | \\ w & = & \ln | a p^{2} H + e^{a r} | + \ln | \frac{Y}{N} | \\ w & = & \ln | (a p^{2} H + e^{a r}) \cdot \frac{Y}{N} | \\ e^{w} & = & (a p^{2} H + e^{a r}) \cdot \frac{Y}{N} \\ (a p^{2} H + e^{a r}) Y & = & e^{w} \cdot N \\ a p^{2} H y + e^{a r} Y & = & e^{w} \cdot N \\ a p^{2} H y & = & e^{w} \cdot N - e^{a r} Y \\ H a p^{2} y & = & N e^{w} - Y e^{a r} \\ H a p p y & = & N e^{w} - Y e^{a r} \end{array}

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*}

Happy New Year Equation

目次

1. Image

2. MathJax

3. source