Question

lg(x-1)^3-3lg(x-3)=6

Answer 1

lg(x-1)³-3lg(x-3)=6
ОДЗ:
$left { {{x-1 textgreater 0} atop {x-3 textgreater 0}} right. , left { {{x textgreater 1} atop {x textgreater 3}} right. = textgreater$
x>3. x∈(3;∞)

lg(x-1)³-lg(x-3)³=6
$lg frac{(x-1) ^{3} }{(x-3) ^{3} } =6$
$lg( frac{x-1}{x-3} ) ^{3} =6$
$( frac{x-1}{x-3} ) ^{3} =10 ^{6}$
$frac{x-1}{x-3}= 10^{2}$
x-1=100*(x-3)
99x=299
x=299/99
299/99∈(3;∞)
⇒

ответ: $x= frac{299}{99}$