Question 6
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 $x \gt 1.$ Find $b.$
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 $x \gt 1.$ Find $b.$