обчислите log₃4 · log₄5 · log₅7 · log₇81

[tex]log_34\cdot log_45\cdot log_57\cdot 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_35\cdot log_581=\frac{log_581}{log_53}=\\\\=log_381=log_33^4=4log_33=4[/tex]