Question

Folosind proprietatile logaritmilor sa se calculeze:
$a) \: log_{6}24 - log_{6}4$
$b) \: log_{3}3 - log_{3} \frac{1}{3}$
$c) \: log_{3}2 + log_{3}6 - log_{3}4$
$d) \: log_{2}14 + log_{2}3 - log_{2}6$
$e) \: \frac{ log_{5}18 - log_{5}2 }{ log_{5}3 }$
$f) \: lg \frac{1}{2} + lg \frac{2}{3} + ..... + lg \frac{9}{10}$
$g) \: log_{2}4 + ( \frac{1}4 ) ^{ - 1} + \sqrt[3]{27}$
$h) \: log_{3}5 + log_{3}6 - log_{3}10$
$i) \: log_{2}5 + log_{2}12 - log_{2}30$

Answer 1

a. log 6 (6)=1 .
b. log 3 (9)=2 .
c. log 3 (3)=1 .
d. log 2 (7) .
e. log 5 (9) / log 5 (3) =2· log 5 (3) / log 5 (3) =2 .
f. lg (1/10) = log 10 (1/10) = log 10 (10 la -1)= -1 .
g. 2+4+3=9 .
h. log 3 (3)=1 .
i. log 2 (2)=1 .