[Fun Maths][Happy New Year]

casperyc 2021-12-31 920

$$ \begin{aligned} w-\ln|ap^2H+\mathrm{e}^{ar}| &= \ln|y|-\ln|N| \\ w &= \ln|ap^2H+\mathrm{e}^{ar}|+\ln\left| \frac{y}{N} \right| \\ w &= \ln\left| \left( ap^2H+\mathrm{e}^{ar} \right) \cdot \frac{y}{N} \right| \\ \mathrm{e}^w &= \left( ap^2H+\mathrm{e}^{ar} \right) \cdot \frac{y}{N} \\ \mathrm{e}^w \cdot N &= \left( ap^2H+\mathrm{e}^{ar} \right) \cdot y \\ \mathrm{e}^w \cdot N &= ap^2Hy+\mathrm{e}^{ar}y \\ ap^2Hy &= \mathrm{e}^w \cdot N - \mathrm{e}^{ar}y \\ Happy &= N\mathrm{e}^w - y\mathrm{e}^{ar} \end{aligned} $$

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