Logaritmos

Calcula los siguientes logaritmos:

$a) \: \log_5{125} \quad b) \: \log_5{\frac{1}{625}} \quad c) \: \log_{\frac{1}{5}}{\frac{1}{125}} \quad d) \: \log{\sqrt[5]{100}}$

SOLUCIÓN

a) $\log_5{125} = \log_5{5^3} = 3$

b) $\log_5{\frac{1}{625}} = \log_5{\frac{1}{5^4}} = \log_5{5^{-4}}=-4$

c) $\log_{\frac{1}{5}}{\frac{1}{125}} = \log_{\frac{1}{5}}{\frac{1}{5^3}} =\log_{\frac{1}{5}}{ \left( \frac{1}{5} \right)^3} =3$

d) $\log {\sqrt[5]{100}} = \log {100^{\frac{1}{5}}}= \log {\left(10^2\right)^{\frac{1}{5}}}= \log {\left(10 \right)^{\frac{2}{5}}} = \frac{2}{5}$