Question

log de 2 na base 3 x log de 3 na base 4 x log de 4 na base 5 x log de 5 na base 6 = ?

Answer 1

$\log_32\cdot\log_43\cdot\log_54\cdot\log_65=\\\\\\\frac{\log_{10}2}{\log_{10}3}\cdot\frac{\log_{10}3}{\log_{10}4}\cdot\frac{\log_{10}4}{\log_{10}5}\cdot\frac{\log_{10}5}{\log_{10}6}=\\\\\\\frac{\log2}{\log3}\cdot\frac{\log3}{\log4}\cdot\frac{\log4}{\log5}\cdot\frac{\log5}{\log6}=\\\\\\\frac{\log2\cdot\log3\cdot\log4\cdot\log5}{\log3\cdot\log4\cdot\log5\cdot\log6}=\\\\\\\frac{\log2}{\log6}$