Question

log по основанию sqrt2 (log 2 3 *log 3 4 )

Answer 1

$log_{sqrt{2}} (log_2 3*log_3 4)=$
$log_a b*log_b c=log_a c$
$log_{sqrt{2}} log_2 4=$
$log(sqrt{2}} log_2 2^2$
$log_a b^n=n*log_a b$
$log_sqrt{2}} (2*log_2 2)=$
$log_a a=1$
$=log_{sqrt{2}} (2*1)=$
$log_{sqrt{2}} 2=$
$log_{sqrt{2}} (sqrt{2})^2$
$2*log_{sqrt{2}} sqrt{2}=$
$2*1=$
$2$
отвте: 2