Question 185316
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \log_{sqrt{x}}(27) = -6]


Remember:


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


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \log_{sqrt{x}}(27) = -6\ \ \Leftrightarrow\ \ sqrt{x}^{-6} = 27]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \ \ \Rightarrow\ \ \frac{1}{sqrt{x}^6}=27\ \ \Rightarrow\ \ \frac{1}{x^3}=27\ \ \Rightarrow\ \ x^3 = \frac{1}{27} \ \ \Rightarrow\ \ x = \sqrt[3]{\frac{1}{27}} = \frac{1}{3}]



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