• Matéria: Matemática
  • Autor: anasantana799
  • Perguntado 9 anos atrás

b) z= log₃ 2 · log₄ 3 · log₅ 4 · log₆ 5 ?

Respostas

respondido por: acidbutter
1
\displaystyle z=\log_32\cdot \log_43\cdot\log_54\cdot\log_65\\\\
z= \frac{\ln2}{\ln3} \cdot \frac{\ln3}{\ln4} \cdot \frac{\ln4}{\ln5} \cdot \frac{\ln5}{\ln6} = \frac{\ln2\ln3\ln4\ln5}{\ln3\ln4\ln5\ln6} =  \frac{\ln2}{\ln6}=\boxed{\log_62}
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