A Simple Problem Thats Not So Simple | A Nice Exponential Equation

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In todays video, I will be teaching you how to solve an exponential problem. Make sure to like, subscribe, and also comment any questions or video ideas you may have relating to math!

#maths #exponents #mathematics #mathstricks #mathchallenge #algebra #equation #problem #challenge #Olympiad #MathOlympiad
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  2. Algebra
  3. Challenge
  4. Equation
  5. Exponents
  6. Math
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Hi again from Arizona!
I just discovered something really interesting. I tried the last equation first by setting 2 to the m and n each equal to 2 to the m and n each over 2 in parenthesis, then squaring each, and setting up a substitution using u and v such that u squared minus v squared factors as (u+v)(u-v), then setting that equal to each of several different factorings of 8064. Solving each of these as a system of equations, I get a range of m and n values, each of which work in the original equation. Your method gives whole number values, but there are lots of other values that work as well.
Thought you might be interested. If you reply with an email address I can scan my work and send it and you can see what I mean.

paulnokleberg
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How do you prove that the two answers are, in fact, equal ? And, incidentally, both answers are meaningless; they don’t tell me any more than the original expression.

larrydickenson