Question 318345
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 81^{5x\,+\,3}\ =\ 243^{3x}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log_3(81^{5x\,+\,3})\ =\ \log_3(243^{3x})]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (5x\,+\,3)\log_3(81)\ =\ (3x)\log_3(243)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (5x\,+\,3)\log_3(3^4)\ =\ (3x)\log_3(3^5)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4(5x\,+\,3)\log_3(3)\ +\ 5(3x)\log_3(3)]


But *[tex \LARGE \log_b(b)_\ =\ 1], so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4(5x\,+\,3)\ =\ 5(3x)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 0.4]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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