Question 623822
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ e^{5x}\ =\ 8900]


Take the natural log of both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ln(e^{5x})\ =\ \ln(8900)]


Use


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log_b\left(x^n\right)\ =\ n\log(x)]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log_b(b)\ =\ 1]


To write


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 5x\ =\ \ln(8900)]


so


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{\ln(8900)}{5}]


Which is a perfectly good answer, but you can also express it as:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \ln\left(\sqrt[5]{8900}\right)]


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