Odpowiedź:
Granica:
[tex]\lim_{x\rightarrow\infty}\left(\frac{3x+2}{x-5}\right) = \lim_{x\rightarrow\infty}\left(\frac{3+\frac{2}{x}}{1-\frac{5}{x}}\right) = 3[/tex]
Zadanie 1.
[tex]6^{2x-1}=1[/tex]
[tex]\log_6(6^{2x-1}) = \log_61[/tex]
[tex]2x-1=0[/tex]
[tex]x = \frac{1}{2}[/tex]
Zadanie 2.
[tex]\log_{x-3}36=2[/tex]
[tex]\frac{\log36}{\log(x-3)}=2[/tex]
[tex]\frac{\log(x-3)}{\log36}=\frac{1}{2}[/tex]
[tex]\log(x-3)=\frac{\log36}{2}= \log{\sqrt{36}} = \log{6}[/tex]
[tex]x-3=6[/tex]
[tex]x=9[/tex]
