Question

o valor de log o,04 125 e igual a:

Answer 1

$log_{0,04} \ 125=log_{ \frac{4}{100}} \ 5^3=3\cdot log_{ \frac{1}{25}} \ 5=3 \cdot log_{ (\frac{1}{5})^2} \ 5\\ \\=3\cdot log_{5^{-2}} \ 5=3\cdot \frac{log_{5} \ 5}{ log_{5} \ 5^{-2}} =3\cdot \frac{log_{5} \ 5}{-2\cdot log_{5} \ 5} =3\cdot \frac{1}{-2\cdot 1}=3\cdot \frac{1}{-2}=-\frac{3}{2}$