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: $x= \frac{299}{99}$