A NICE TRICK SOLUTION TO 1^x = 6 | EXPONENTIAL EQUATION | CAN YOU SOLVE?

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Explore the fascinating world of exponential equations with varying bases and unlock the power of exponentiation! In this educational video, we delve into the concept of exponential equations where the base is not a constant value. Learn the fundamentals, discover the properties, and master solving equations with different bases, all explained in a clear and concise manner. Join us on this exponential journey and level up your mathematical prowess!
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[@allozovsky]

But that would never be on a principal branch anyway, so it's a little bit "illegal" (say, Wolfram Mathematica would never give a solution to such an "equation").

[@SidneiMV]

Let's try 1^x = -6 (2kπi)x = ln6 + ln(-1) = ln6 + (1 + 2q)πi x = [ln6 + (1 + 2q)πi]/2kπi *x = (1/2k)[1 + 2q -i(ln6)/π]* for example x = (1/2)[1 -i(ln6)/π] e^{(2πi)(1/2)[1 -i(ln6)/π]} = e^{(πi)[1 -i(ln6)/π]} = e^(πi)e^[-πi²(ln6)/π] = (-1)e^ln6 = -6

[@allozovsky]

Well, seems to be correct. At least for the first branch.

[@Alamaths]

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