Question

Найти значение выражения

Answer 1

$log^2_627+\frac{3log_612^3}{log_{108}6}=(log_63^3)^2+\frac{3\cdot3log_612}{\frac{1}{log_6108}}=$

$(3log_63)^2+9log_612\cdot log_6108=9log_6^23+9log_612\cdot log_6(9\cdot12)=$

$9log_6^23+9log_612\cdot (log_69+log_612)=9\left[log_6^23+log_612\cdot (log_69+log_612)\right] =$

$9(log_6^23+log_612\cdot log_69+log_6^212) =]9(log_6^23+log_612\cdot log_63^2+log_6^212) =$

$9(log_6^23+2log_612\cdot log_63+log_6^212) =9(log_63+log_612)^2 =9\left[log_6(3\cdot12)\right]^2 =$

$9(log_636)^2 =9(log_66^2)^2 =9 \cdot (2log_66)^2 =9 \cdot (2)^2 =9 \cdot 4=36$