Question

1 ) Reduza as expressões em logaritmo decimais;

a) $log_{12}$2 + $log_{12}$4

b) $log_{9}$24 - $log_{9}$6

c) $log_{2$3 + $log_{2$ 1 $- log_{2$ 7

Answer 1

$a)log _{12} ^{2} +log _{12} ^{4} =log _{12} ^{2.4} =log _{12} ^{8} = \frac{log8}{log12} = \frac{log2^3}{log2^2.3} = \frac{3log2}{2og2+log3} = \\ \frac{3.0,3010}{2.0,3010+0,4771}= \frac{0,903}{1.0791} =0,8368 \\ b)log _{9} 24-log _{9} 6=log _{9} \frac{24}{6} =log _{9}4= \frac{log4}{log9} = \frac{log2^2}{log3^2} = \frac{2log2}{3log3} = \frac{2.0,3010}{3.0,4771} = \\ \frac{0,602}{1,4313} =0,4206 \\ c)log _{2} 3 + log _{1} - log _{2} 7= log _{2} + 0-log _{2} 7=log _{2 \frac{3}{7} }= \\ log3:log7$