Question 690227
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There are a number of ways to go about this one, but this way is rather tidy.  Use your built-in Windows or Mac scientific calculator if you need a numeric approximation.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3^x\ =\ 2^{x\ -\ 1}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\log_2(3)\ =\ (x\ -\ 1)\log_2(2)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\log_2(3)\ =\ x\ -\ 1\ \ ]because *[tex \LARGE \log_b(b)\ =\ 1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x(\log_2(3)\ -\ 1)\ =\ -1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{-1}{\log_2(3)\ -\ 1}]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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