Aloha :)
$$\small f(x)=\frac{\ln(4x^4)}{\ln(6x^3)}=\frac{\ln(4)+\ln(x^4)}{\ln(6)+\ln(x^3)}=\frac{\ln(4)+4\ln(x)}{\ln(6)+3\ln(x)}=\frac{\pink{\frac{1}{\ln(x)}}\cdot\left(\ln(4)+4\ln(x)\right)}{\pink{\frac{1}{\ln(x)}}\cdot\left(\ln(6)+3\ln(x)\right)}=\frac{\frac{\ln(4)}{\ln(x)}+4}{\frac{\ln(6)}{\ln(x)}+3}$$Für \(x\to\infty\) wächst \(\ln(x)\to\infty\), sodass$$\lim\limits_{x\to\infty}f(x)=\frac{0+4}{0+3}=\frac43$$
