2019 AIME II Problem 6

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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.