Lista de exercícios do ensino médio para impressão
Desenvolver as expressões abaixo aplicando as propriedades dos logaritmos.
a)
$\;log_{{}_{\Large \,5\,}}(\dfrac{\,5a\,}{bc})\,$
b)
$\;log_{{}_{\Large \,3\,}}(\dfrac{\,ab^2\,}{c})\,$
c)
$\;log_{{}_{\Large \,2\,}}\left(\dfrac{\,a^2\,\sqrt{\,b\,}\,}{\sqrt[\large \,3\,]{\,c\,}} \right)$
d)
$\;log_{{}_{\Large \,3\,}}\left(\dfrac{\,a\,\centerdot\,b^3\,}{c\,\centerdot\,\sqrt[\large \,3\,]{\,a^2\,}}\right)\,$

e)
$\;log\sqrt{\dfrac{\,ab^3\,}{c^2}}\,$
f)
$\;log_{{}_{\Large \,3\,}}\sqrt[\Large 3\,]{\dfrac{\,a\,}{\,b^2\,\centerdot\,\sqrt{\,c\,}}}\,$

g)
$\;log_{{}_{\Large \,2\,}}\sqrt{\dfrac{\,4a\,\sqrt{\,ab\,}}{\,b\;\sqrt[\Large 3\,]{\,a^2b\,}}}\,$

h)
$\;log\,\left(\sqrt[\LARGE 3\,]{\dfrac{\,a^{\large 4}\,\sqrt{\,ab\,}}{\,b^2\;\sqrt[\Large 3\,]{\,bc\,}}}\right)^{\Large 2}\,$

resposta: a) $\,1\,+\,log_5a\,-\,log_5b\,-log_5c\,$ b) $\,log_3a\,+\,2\,log_3b\,-\,log_3c\,$ c) $2\,log_2a\,+\,\frac{1}{2}log_2b\,-\,\frac{1}{3}log_2c$ d) $\,\frac{1}{3}\,log_3a\,+\,3\,log_3b\,-\,log_3c$ e) $\frac{1}{2}\,log\,a\,+\,\frac{3}{2}log\,b\,-\,log\,c$ f) $\frac{1}{3}\,log\,a\,-\,\frac{2}{3}log\,b\,-\,\frac{1}{6}log\,c$ g) $\,2\,+\,\frac{5}{12}log_2a\,-\,\frac{5}{12}log_2b\,$h) $\,3\,log\,a\,-\,\frac{11}{9}log\,b\,-\,\frac{2}{9}log\,c\,$
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Veja exercÍcio sobre: propriedades dos logaritmos