ah, so the $\displaystyle

x=exp\left(\frac{\ln 5 \cdot \ln 3}{\ln 7}+\frac{\ln 7 \cdot \ln 3}{\ln 4}\right) \approx 11.59699220980753

$ that I quoted really should have been

$\displaystyle

x=exp^{\left(\frac{\ln 5 \cdot \ln 3}{\ln 7}+\frac{\ln 7 \cdot \ln 3}{\ln 4}\right)} \approx 11.59699220980753

$