1)
Z definicji logarytmu:
[tex]log_{a}b = c \ \ to \ \ a^{c} = b\\\\log_{8}4 = x\\\\8^{x} = 4\\\\(2^{3})^{x} = 2^{2}\\\\2^{3x} = 2^{2}\\\\3x = 2 \ \ /:3\\\\x = \frac{2}{3}\\\\log_{8}4 = \frac{2}{3}\\\\Odp. \ d)[/tex]
2)
[tex]|\sqrt{3}-4| = -(\sqrt{3}-4) =4 - \sqrt{3} \approx4 - 1,7 \approx 2,3\\\\|\sqrt{3}-4| \in \ <2,3; 4>\\\\Odp. \ b)[/tex]
3.
[tex]\frac{x}{2}+2 < \frac{x}{3} \ \ /\cdot6\\\\3x+12 < 2x\\\\3x-2x < -12\\\\x < -12\\\\x \in \ (-\infty; -12)\\\\Odp. \ a)[/tex]
