A Quick and EZ Tetration Problem 😄

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This problem is from Nonroutine Problems in Algebra, Geometry and Trigonometry:

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How would you use tetration with logarithms?

erikroberts
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Suggestion:
Find all real values a, b and c, such that (a^b)^c=a^(b^c)

renyxadarox
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New Math, I call them. They are not weird they are just uncommon. Examples like this get one to have to rethink math in a similar way as those humans who have developed the foundations of modern math through the centuries. I applaude your initiative.

lewebusl
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Buenas tardes Señores: SyberMath, reciban un cordial saludo, apoyo esta iniciativa, es necesario entender bien para poder aprender, y la única forma de lograrlo es haciendo y documentando un procedimiento. por favor espero más ejercicios de este tipo. Éxitos.

maxwellarregui
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X
X
X=X to the third pentation

RyanLewis-Johnson-wqxs
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Find the inverse function of
Y =2^x +3^x

DJ.Nihad
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More problems would be interesting, especially if there was a more general method of solution.

old_Army_guy
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If there is 65536 in RHS then x = 4 because
2^{2^(2^2)} = 2^(2^4) = 2^16 = 65536

raghvendrasingh