Question

Вычислить: log3((log2 5)*(log5 8)

Answer 1

По формулам:
$log_ab=\frac{1}{log_ba}\\\frac{log_ca}{log_cb}=log_ba$

$log_3(log_25*log_58)=log_3(\frac{1}{log_52}*log_58)=log_3(\frac{log_58}{log_52})=log_3(log_28)=\\=log_3(log_22^3)=log_33=1$

Answer 2

log₃((log₂5)*(log₅8)=log₃((log₂5)*(log₅2³)=log₃((log₂5)*(3*log₅2)=
=log₃(3*log₂5*log₅2)=log₃(3*log₂5*/log₂5)=log₃3=1.