Question

calcular el logaritmo de 4/9 en base 27/8

Answer 1

$log_{ \frac{27}{8}} \frac{4}{9}= x \\ \\ ( \frac{27}{8}) ^x= (\frac{4}{9}) \\ \\ ( \frac{3^3}{2^3}) ^x= (\frac{2^2}{3^2}) \\ \\ (( \frac{3}{2})^3)^x= (\frac{2}{3})^2 \\ \\ (( \frac{3}{2})^3)^x= (\frac{3}{2}) ^{-2} \to entonces \to 3x=-2 \to x= \frac{-2}{3} \\ \\ \boxed{log_{ \frac{27}{8}} \frac{4}{9}= x \to log_{ \frac{27}{8}} \frac{4}{9}= \frac{-2}{3}}$

Espero que te sirva, salu2!!!!