Is this not a proof of Fermat’s Last Theorem?

I’m wanted to play around with Fermat’s Last Theorem, and the proof seemed very obvious to me! Find the errors!

An + Bn ≠ Cn if A, B, C are whole numbers and n > 2.

Let’s try for a reductio ad absurdum. Let’s put Fermat’s claim in logarithmic form.

  1. loga X + logb Y = logc Z in which all terms equal n, n > 2.
  2. If a, b, and c are whole numbers all raised to the same power n then we can rewrite the above.
  3. (logc X / logc A) + (logc Y / logc B) = logc Z. Converting to the same base.
    1. Side notes:
    1. log5 9/ log5 3 + log5 16 / log5 4 = log5 25
    2. log5 (9/3 * 16/4) = log5 25
    3. logc (XY/AB) = logc Z
    1. (XY/AB) = Z
  4. (logc X / logc A) = (logc Y / logc B). Since all terms equal n.
  5. (logc X / logc A)/ (logc Y / logc B) = 1.
  6. (logc X / logc A) + (logc Y / logc B) = 2.

But we already said n > 2, thus logc Z cannot be greater than 2.

[Hahah! The errors here are super obvious!]

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