Happy New Year Calculation

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If the following is true,

$$w+ln\left|N\right|=ln\left|y\right|+ln|aH{p}^2-e^{ar}-\frac{{45}^2-1^2}{y}|$$

then

$$w=ln\left|\right(y)(aH{p}^2-e^{ar}-\frac{2025-1}{y}\left)\right|-ln\left|N\right|$$ $$\Rightarrow w=ln\left|\right(\frac{y}{N})(aH{p}^2-e^{ar}-\frac{2024}{y}\left)\right|$$ $$\Rightarrow {\mathrm{e}}^w=\left(\frac{y}{N}\right)(aH{p}^2-e^{ar}-\frac{2024}{y})$$ $$\Rightarrow {\mathrm{e}}^w=\frac{aH{p}^{2}y}{N}-\frac{e^{ar}y}{N}-\frac{2024}{N}$$ $$\Rightarrow {\mathrm{e}}^{w}N=aH{p}^{2}y-e^{ar}y-2024$$

... to you all.

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