Question 240290
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y = \log_b(x) \ \ \Rightarrow\ \ b^y = x]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10^2\ =\ xy]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log_b(x) + \log_b(y) = \log_b(xy)]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10^2\ =\ \frac{4y}{x}]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ xy\ =\ \frac{4y}{x}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ =\ 4]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \pm2]


If *[tex \LARGE x\ =\ 2], then *[tex \LARGE y\ =\ \frac{100}{2}\ =\ 50].


If *[tex \LARGE x\ =\ -2], then *[tex \LARGE y\ =\ \frac{100}{-2}\ =\ -50].



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