18. (12 points) As shown in the figure, the right prism $A B C D - A _ { 1 } B _ { 1 } C _ { 1 } D _ { 1 }$ has a rhombus base, with $A A _ { 1 } = 4 , A B = 2 , \angle B A D = 60 ^ { \circ }$ . Let $E , M , N$ be the midpoints of $B C$ , $B B _ { 1 Therefore $f(x)$ has a unique zero point on $\left[\frac{\pi}{2}, \pi\right]$. (iv) When $x \in (\pi, +\infty)$, $\ln(x+1) > 1$, so $f(x) < 0$, thus $f(x)$ has no zero points on $(\pi, +\infty)$. In conclusion, $f(x)$ has exactly 2 zero points.
Solution:
18. (12 points)\\
As shown in the figure, the right prism $A B C D - A _ { 1 } B _ { 1 } C _ { 1 } D _ { 1 }$ has a rhombus base, with $A A _ { 1 } = 4 , A B = 2 , \angle B A D = 60 ^ { \circ }$ . Let $E , M , N$ be the midpoints of $B C$ , $B B _ { 1
Therefore $f(x)$ has a unique zero point on $\left[\frac{\pi}{2}, \pi\right]$.\\
(iv) When $x \in (\pi, +\infty)$, $\ln(x+1) > 1$, so $f(x) < 0$, thus $f(x)$ has no zero points on $(\pi, +\infty)$.
In conclusion, $f(x)$ has exactly 2 zero points.