e^π or π^e: Which Is Bigger?

Which is bigger: e^π or π^e? Most people guess wrong, and you can't just reason it out with "bigger base wins" or "bigger exponent wins." In this video, Chalkalong, the AI math tutor I'm building, works through it step by step on a live whiteboard. The trick is to take the log of both sides, rewrite everything in terms of one function, f(x) = ln(x)/x, and use calculus to find where that function peaks. What you'll see: Why swapping base and exponent can go either way Taking logs to compare exponents Using the quotient rule to find the maximum of ln(x)/x The graph that makes the answer obvious Answer: e^π ≈ 23.14 is bigger than π^e ≈ 22.46. Challenge: which is bigger, 3^π or π^3? Comment your answer 👇 Try Chalkalong: chalkalong.com #math #calculus #ePi #mathpuzzle #AI #mathtutor #edtech #chalkalong