10. Let $a$ be a real number greater than 1. Consider the functions $f(x) = a^x$ and $g(x) = \log_a x$. Which of the following options are correct? (1) If $f(3) = 6$, then $g(36) = 6$ (2) $\frac{f(238)}{f(219)} = \frac{f(38)}{f(19)}$ (3) $g(238) - g(219) = g(38) - g(19)$ (4) If $P, Q$ are two distinct points on the graph of $y = g(x)$, then the slope of line $PQ$ must be positive (5) If the line $y = 5x$ and the graph of $y = f(x)$ have two intersection points, then the line $y = \frac{1}{5}x$ and the graph of $y = g(x)$ also have two intersection points
& 1，2，4，5 & & 21 & 6 & & 41 & 3
10. Let $a$ be a real number greater than 1. Consider the functions $f(x) = a^x$ and $g(x) = \log_a x$. Which of the following options are correct?\\
(1) If $f(3) = 6$, then $g(36) = 6$\\
(2) $\frac{f(238)}{f(219)} = \frac{f(38)}{f(19)}$\\
(3) $g(238) - g(219) = g(38) - g(19)$\\
(4) If $P, Q$ are two distinct points on the graph of $y = g(x)$, then the slope of line $PQ$ must be positive\\
(5) If the line $y = 5x$ and the graph of $y = f(x)$ have two intersection points, then the line $y = \frac{1}{5}x$ and the graph of $y = g(x)$ also have two intersection points