Question 14Let $a \gt 1$ and $x \gt 1$ satisfy $\small \log_a\!\left(\log_a\!\left(\log_a 2\right) + \log_a 24 - 128\right)$ $= 128$ and $\log_a\!\left(\log_a x\right) = 256.$ Find the remainder when $x$ is divided by $1000.$