In a Martian civilization, all logarithms whose bases are not specified as assumed to be base \(b\), for some fixed \(b\ge2\). A Martian student writes down\[3\log(\sqrt{x}\log x)=56\]\[\log_{\log x}(x)=54\]and finds that this system of equations has a single real number solution \(x>1\). Find \(b\).