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

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    • if x+y=8, find the max of x^y (Lamber...  
More about the Lambert W function:    • Lambert W Function (domain, range, ap...  

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