Brazil | A Nice Exponential Equation | Math Olympiad

Brazil | A Nice Exponential Equation | Math Olympiad
we are solve the nice exponential equation and find out the right answer
#olympiadmathematics #olympiadpreparation #olympiad
@MathWithKhan-ki8po
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[@unemiryune9322]

step 1: is it 1? step 2: is it 2 or more? step 3: well it can't be 0 step 4: must be 0,5 solved in 15 secs

[@aykutuzd]

Take ln2 of both sides

[@vladnovikoff7152]

Why so difficult. Each side to the power of 1/m and that's it.

[@3_14pie]

I made it be m4^m = 1 so m must be less than 1 and m2^m2 = 1 ignoring the infinite recursion, it can only be 2

[@xinpingdonohoe3978]

If m is an integer, then it's got to be a power such that 4^m is rational. Positive integers make 1/m too small. Negative integers make 1/m negative. 0 is bad. Then it's got to be a fraction. To remain rational, the denominator must be 1 or 2. 1 failed, so we try 1/2. It works. Imagine the graphs, it's the only solution. So m=2.

[@xinpingdonohoe3978]

I meant m=1/2 at the end.