diff --git a/notes/sections/2.md b/notes/sections/2.md index bb679d0..7fda7f2 100644 --- a/notes/sections/2.md +++ b/notes/sections/2.md @@ -249,8 +249,8 @@ $W$ both sides. \begin{align*} \frac{5 \sqrt{2 \pi}}{12 \sqrt{x}} e^{-8x} = 10^{-D} & \thus \left(\frac{12}{5}\right)^2 \frac{x}{2 \pi} e^{16x} = 10^{2D} \\ - & \thus 16x e^{16x} = \left(\frac{5 \pi}{9}\right)^2 10^{2D + 1} \\ - & \thus x = \frac{1}{16} W\left(\left(\frac{5 \pi}{9}\right)^2 10^{2D + 1}\right) + & \thus 16x e^{16x} = \frac{5 \pi}{9} 10^{2D + 1} \\ + & \thus x = \frac{1}{16} W\left(\frac{5 \pi}{9} 10^{2D + 1}\right) \end{align*} The smallest integer which satisfies the inequality is then $$