Question

In(7x+2)=in(5x-20) log5^2x-log5x=0 log3(3x-1)> 3

Answer 1

1) 
$\displaystyle Ln(7x+2)=Ln(5x-20)\\\\ODZ: \left \{ {{7x+2\ \textgreater \ 0} \atop {5x-20\ \textgreater \ 0}}; \left \{ {{x\ \textgreater \ - \frac{2}{7}} \atop {x\ \textgreater \ 4}} \right. \right.\\\\x\in (4;+oo)\\\\7x+2=5x-20\\\\2x=-22\\\\x=-11$
решений нет 
х=-11 не входит в ОДЗ

2) 
$\displaystyle log_5^2x-log_5x=0\\\\ODZ: x\ \textgreater \ 0\\\\log_5x(log_5x-1)=0\\\\log_5x=0; x=5^0; x=1\\\\log_5x=1; x=5^1;x=5$

ответ х=1 или х=5

3) 
$\displaystyle log_3(3x-1)\ \textgreater \ 3\\\\ODZ: 3x-1\ \textgreater \ 0; x\ \textgreater \ 1/3\\\\3x-1\ \textgreater \ 3^3\\\\3x-1\ \textgreater \ 27\\\\3x\ \textgreater \ 28\\\\x\ \textgreater \ 9 \frac{1}{3}$

ответ x∈ (9¹/₃; +∞)