Questions: log(2/3) (8/27) + log(1/3) 27 + log(1/5) 25

To solve the given logarithmic expression, we can use the change of base formula to convert each logarithm to a common base (e.g., base 10 or base e). This will allow us to compute the values using Python's math library.

Usamos la fórmula de cambio de base para convertir cada logaritmo a una base común, por ejemplo, base 10: \[ \log_b(a) = \frac{\log_k(a)}{\log_k(b)} \]

Calculamos cada logaritmo utilizando la fórmula de cambio de base: \[ \log_{\frac{2}{3}} \frac{8}{27} = \frac{\log \left( \frac{8}{27} \right)}{\log \left( \frac{2}{3} \right)} \approx 3.000 \] \[ \log_{\frac{1}{3}} 27 = \frac{\log 27}{\log \left( \frac{1}{3} \right)} \approx -3.000 \] \[ \log_{\frac{1}{5}} 25 = \frac{\log 25}{\log \left( \frac{1}{5} \right)} \approx -2.000 \]

Sumamos los resultados obtenidos: \[ 3.000 + (-3.000) + (-2.000) = -2.000 \]

\[ \boxed{-2.000} \]