TITLE: comparing the two values
QUESTION [0 upvotes]: Suppose $0<a<1$ and $x>0$. The symbol $int(x)$ returns the maximum integer that is no greater than $x$. Would someone tell us which of the following two values is larger?

$3 \times int({\log}_2 \log_a x)$
$2 \times int({\log_a x})-2$

REPLY [1 votes]: Let $X=\log_a x$. Here I drew the graph of $Y=3\lfloor\log_2 X\rfloor$ (red line) and $Y=2\lfloor X\rfloor -2$ (blue line). Note that if $X$ is sufficiently large, $X\gg\log_2 X$.
{"set_name": "stack_exchange", "score": 0, "question_id": 1132590}