If x^y=8 and x is bigger than 1, then what's the minimum of x+y=? @blackpenredpen

Uploaded January 2025 | Updated September 2026, 2 weeks ago

If x^y=8 and x is bigger than 1, find the minimum of x+y. At first, you might notice 2^3=8 and 2+3=5 and that will be the answer, however, what if x is not a whole number? This seemingly easy calculus 1 optimization problem requires the Lambert W function to find its exact value. This question is similar to my previous video youtu.be/zdAJXil-NvA?si=vJ95sudIGXpua6D0
More about the Lambert W function: youtu.be/Qb7JITsbyKs?si=-sBLaf12qel9llEZ

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