If

\( z = \frac{1}{2} [ e^{\ln (5\pi)} + \log(9) - \pi \ln(e^{3}) - \log(3) + \ln(2) \log(e) ] \),

where \(\ln\) is the natural logarithm and \(\log\) is the common logarithm,

and considering that \( \frac{\ln(6)}{\ln(10)} \approx 0.78\), \(\pi \approx 3.14\), \(\sqrt {11} \approx 3.316\) and \(\sqrt {13} \approx 3.605\)

Then, is valid that...

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