Răspuns:
b) [tex] lg 0,01 = lg \frac{1}{100} = lg 10^{-2} = -2 lg 10 = -2. [/tex]
[tex]2^{\log_2 3}= 3[/tex]
[tex]9^{\log_3 5} = (3^2)^{\log_3 5}=3^{2\cdot \log_3 5}=(3^{\log_3 5})^2=5^2=25[/tex]
-2+3-25=-24.
c) [tex] \log_2 3 \cdot \log_3 5 \cdot \log_5 8 = \log_2 3 \cdot \frac{\log_2 5}{\log_2 3}\cdot\frac{\log_2 8}{\log_2 5}=\log_2 8 = \log_2 2^3 = 3[/tex]
d) [tex] \log_3 5 \log_7 11 = \log_3 5 \frac{\log_3 11}{\log_3 7} = \frac{\log_3 5 \log_3 11}{\log_3 7} [/tex]
[tex] \log_7 5 \log_3 11 = \frac{\log_3 5}{\log_3 7}\log_3 11 = \frac{\log_3 5 \log_3 11}{\log_3 7} [/tex]
Deci fractia aia = 1.
Explicatie:
[tex]x=\log_a y[/tex] este echivalent cu [tex]a^x = y[/tex]. (Functia logaritm este inversa functiei exponentiale)
Pentru [tex]a=2, y=3, x=\log_a y= \log_2 3[/tex] rezulta [tex]2^{\log_2 3}=3[/tex].
