Zad. 1
[tex]a = log_3 \ \frac{1}{9} \\ 3^a = \frac{1}{9} \\ 3^a = \frac{1}{3^2} \\ 3^2 = 3^{-2} \\ a = - 2 \\\\ b = log_3 \ 3 \\ b = 1 \\\\ c = log_3 \ \frac{1}{27} \\ 3^c =\frac{1}{27} \\ 3^c =\frac{1}{3^3} \\ 3^c =3^{-3} \\ c = -3 \\\\ - 3 < - 2 < 1 \\ c < a < b[/tex]
Odp. D
Zad. 2
[tex]8log_4 \ 2 + 2 = 8log_4 \ \sqrt{4} + 2 =8log_4 \ 4^{\frac{1}{2}}+ 2 =\not{8}^4 \cdot \frac{1}{\not{2}_1} log_4 \ 4+ 2 =4 \cdot 1 + 2 = \\ = 4+2=6[/tex]
Odp. B
Zad. 3
[tex]log_3 \ x = 9 \\ Z \ de f inicji \ logarytmu: \\ x > 0 \ i \ x = 3^9[/tex]
Odp. C
Zad. 4
[tex]log_5 \ 5 - log_5 \ 125 = 1 - log_5 \ 5^3 = 1 - 3log_5 \ 5 = 1 - 3 \cdot 1 = 1 - 3 = -2[/tex]
Odp. A
Zad. 5
[tex]log_4 \ 8 + log_4 \ 2 = log_4 \ (8 \cdot 2) = log_4 \ 16 = log_4 \ 4^2 = 2log_4 \ 4 = 2 \cdot 1 = 2[/tex]
Odp. B
