Question 313566
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I'm going to presume you mean


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log_x\left(\frac{1}{4}\right)\ =\ -\frac{2}{3}]


Use the definition of the logarithm function:


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


So you can write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -\frac{2}{3} = \log_x\left(\frac{1}{4}\right) \ \ \Rightarrow\ \ x^{-\frac{2}{3}}\ =\ \frac{1}{4}]



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \sqrt[3]{4^2}\ =\ \sqrt[3]{16}\ =\ 2\sqrt[3]{2}]


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