2019 AIME II Problem 6

In a Martian civilization, all logarithms whose bases are not specified are assumed to be base b, for some fixed b \geq 2. A Martian student writes down

\begin{aligned} 3 \log (\sqrt{x} \log x) & =56 \\ \log _{\log (x)}(x) & =54 \end{aligned}

and finds that this system of equations has a single real number solution x>1. Find b.