Logarithm 7

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...