Question 93
Find all values of the real parameter $a$ such that the inequality
$$
\log_a(a^x + 1) + \frac{1}{\log_{a^x-1} a} \le x - 1 + \log_a(a^2 - 1)
$$
holds true for every $x \in (0, 1]$.
$$
\log_a(a^x + 1) + \frac{1}{\log_{a^x-1} a} \le x - 1 + \log_a(a^2 - 1)
$$
holds true for every $x \in (0, 1]$.