Solving t^t = 49 | Harvard Math Tournament Problem скачать в хорошем качестве

Solving t^t = 49 | Harvard Math Tournament Problem

This problem appeared on the Harvard-MIT Math Tournament, and it's trickier than it looks. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Your first instinct? Try t = 7 since 49 = 7² But 7^7 = 823,543... way too big! 🚫 The real answer requires a special function that most people have never seen: the Lambert W function. Watch how we: 📐 Visualize the curve 🔄 Transform the equation using logarithms ✨ Apply the Lambert W function ✅ Get the exact closed-form solution ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Timestamps: 0:00 The Problem 0:26 Graph Visualization 1:11 Analytical Solution 2:23 Lambert W Function 3:55 Final Answer: t ≈ 3.278 4:17 Key Takeaway The answer? t ≈ 3.238 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 🔔 Subscribe for more visual mathematics @dailymathvisuals 📱 Instagram: @dailymathvisuals 🎵 TikTok: @dailymathvisuals patreon:   / dailymathvisuals   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 🎨 Get these visuals as 4K wallpapers: patreon.com/dailymathvisuals ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ #math #mathematics #harvard #mit #mathtournament #lambertw #mathproblem #calculus #algebra #mathvisualization #education #stem #learning