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Algebra Level 5

Find the domain of the function

\[ \LARGE f(x) = \log_{ \frac {3}{2} } \left ( \log_{ \frac{1}{2}} \left ( \log_{\pi} \left ( \log_{\frac {\pi}{4} } x \right ) \right ) \right ) \]

Details and Assumptions:

Domain of a function \(f(x)\) means the permissible values of \(x\) for which the function is real-valued defined.

\({\frac{3}{2},\frac{1}{2},\pi,\frac{\pi}{4}}\) are the bases of their corresponding logarithms

\(x\) is the coefficient of the logarithm with base \( \frac {\pi}{4} \)

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