In a Martian civilization, all logarithms whose bases are not specified are assumed to be base $b$, for some fixed $b \ge 2$. 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 $b$.

Let's think step by step and output the final answer within \boxed{}.
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