Question 234463
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First use:


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


So


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log(x^9)\ =\ 9\log(x)\ =\ \frac{1}{2}]


And


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log(x)\ =\ \frac{1}{18}]


Now use


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


and the fact that if the base is not specified, base 10 is understood to write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 10^{\frac{1}{18}]


But


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a^{\frac{n}{m}} = \sqrt[m]{a^n}]


So


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \sqrt[18]{10}]


That's the exact answer.  Use your calculator if you need a numeric approximation.



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