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Algebra Level 5

Find the domain of the function

f(x)=log32(log12(logπ(logπ4x))) \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)f(x) means the permissible values of xx for which the function is real-valued defined.

32,12,π,π4{\frac{3}{2},\frac{1}{2},\pi,\frac{\pi}{4}} are the bases of their corresponding logarithms

xx is the coefficient of the logarithm with base π4 \frac {\pi}{4}

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