Question 880083
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3^{2x}\ =\ 5]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ln\left(3^{2x}\right)\ =\ \ln(5)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x\ln(3)\ =\ \ln(5)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{\ln(5)}{2\ln(3)}\ =\ \frac{\ln(5)}{\ln(9)}]


This can be done slightly more elegantly so long as you either have a calculating device that will find base 3 logs, or you don't care to find a numerical approximation for your answer.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3^{2x}\ =\ 5]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log_3\left(3^{2x}\right)\ =\ \log_3(5)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x\log_3(3)\ =\ \log_3(5)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{\log_3(5)}{2}]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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