Answer :
Notice that:
[tex]\lim _{x\rightarrow+\infty}\log (x)=+\infty[/tex]Therefore:
[tex]\lim _{x\rightarrow+\infty}(-\log (x)+4)=-\lim _{x\rightarrow+\infty}\log (x)+4=-\infty+4=-\infty[/tex]Notice that:
[tex]\lim _{x\rightarrow+\infty}\log (x)=+\infty[/tex]Therefore:
[tex]\lim _{x\rightarrow+\infty}(-\log (x)+4)=-\lim _{x\rightarrow+\infty}\log (x)+4=-\infty+4=-\infty[/tex]