Question

Логорифм???????????????????????????????????????

Answer 1

$log_213+2=log_2(7x-4),$

ОДЗ: $7x-4 textgreater 0,\7x textgreater 4,\x textgreater frac{4}{7}.$

$log_213-log_2(7x-4)=-2,\\log_2{left(frac{13}{7x-4}right)}=-2,\\log_2{left(frac{13}{7x-4}right)}=log_2{frac{1}{4}},\\frac{13}{7x-4}=frac{1}{4},\\frac{13}{7x-4}-frac{1}{4}=0,\\frac{13cdot4-(7x-4)}{4(7x-4)}=0,\\frac{52-7x+4}{4(7x-4)}=0,\\56-7x=0,\\7x=56,$

$x=8$ — удовлетворяет ОДЗ.

Ответ: $x=8$.