Question

обчислите log₃4 · log₄5 · log₅7 · log₇81

Answer 1

$log_34cdot log_45cdot log_57cdot log_781=(frac{1}{log_43}cdot log_45)cdot (frac{1}{log_75}cdot log_781)=\\= frac{log_45}{log_43}cdot frac{log_781}{log_75}= [, log_{a}{b}=frac{log_{c}b}{log_{c}a}, ]=log_35cdot log_581=frac{log_581}{log_53}=\\=log_381=log_33^4=4log_33=4$