Question

Ex 20 din poza cu cele 3 subpuncte.

Answer 1

Răspuns:

b) $lg 0,01 = lg \frac{1}{100} = lg 10^{-2} = -2 lg 10 = -2.$

$2^{\log_2 3}= 3$

$9^{\log_3 5} = (3^2)^{\log_3 5}=3^{2\cdot \log_3 5}=(3^{\log_3 5})^2=5^2=25$

-2+3-25=-24.

c) $\log_2 3 \cdot \log_3 5 \cdot \log_5 8 = \log_2 3 \cdot \frac{\log_2 5}{\log_2 3}\cdot\frac{\log_2 8}{\log_2 5}=\log_2 8 = \log_2 2^3 = 3$

d) $\log_3 5 \log_7 11 = \log_3 5 \frac{\log_3 11}{\log_3 7} = \frac{\log_3 5 \log_3 11}{\log_3 7}$

$\log_7 5 \log_3 11 = \frac{\log_3 5}{\log_3 7}\log_3 11 = \frac{\log_3 5 \log_3 11}{\log_3 7}$

Deci fractia aia = 1.

Explicatie:

$x=\log_a y$ este echivalent cu $a^x = y$. (Functia logaritm este inversa functiei exponentiale)

Pentru $a=2, y=3, x=\log_a y= \log_2 3$ rezulta $2^{\log_2 3}=3$.