$$ \begin{aligned} & \lim _{x \rightarrow 0}\left[\left(\frac{1-\cos ^2(3 x)}{\cos ^3(4 x)}\right)\left(\frac{\sin ^3(4 x)}{\left(\log _e(2 x+1)\right)^5}\right)\right] \\\\ & =\lim _{x \rightarrow 0}\left[\frac{1-\cos ^2(3 x)}{9 x^2} \times \frac{9 x^2}{\cos ^3(4 x)}\right] \times \frac{\frac{\sin ^3 4 x}{(4 x)^3} \times 64 x^3}{\left[\frac{\log _e(2 x+1)}{2 x}\right]^5 \times(2 x)^5} \\\\ & =\left[\frac{1 \times 9 \times 1}{(1)}\right] \times\left[\frac{1 \times 64}{1 \times 32}\right] \\\\ & =9 \times 2=18 \end{aligned} $$