Question

se log a 2:m e log a 3:n, entao log(1/ a)(2/3) vale?

Answer 1

Propriedades :

*$log_{a}b = \frac{logb}{loga}$
*log(a/b) = loga - logb

Calculando :

$log_{ \frac{1}{a} } (\frac{2}{3}) = \frac{log \frac{2}{3} }{log \frac{1}{a} }$

$log_{ \frac{1}{a} } ( \frac{2}{3} ) = \frac{log2-log3}{log1-loga} = \frac{log2-log3}{-loga} = \frac{log3-log2}{loga}$

$log_{ \frac{1}{a} } (\frac{2}{3}) = \frac{log3}{loga} - \frac{log2}{loga}$

$log_{ \frac{1}{a} } (\frac{2}{3}) = log_{a}3 - log_{a}2$

$log_{ \frac{1}{a} } (\frac{2}{3}) = n-m$