Question

Log1/3(2x-1)=log 3(1/x+3)Решите уравнение

Answer 1

Log₃(1/x)+log₃√x=-1

ОДЗ:
{(1/x)>0     {x>0
 √x>0         x>0
ОДЗ: x∈(0;∞)

log₃x⁻¹+log₃x¹/²=-1
-1*log₃x+(1/2)*log₃x=-1
(-1/2)*log₃x=-1
log₃x=2
x=3²
x=9