Question

log 2x-1 (2x-3) = log 2x-3 (2x-1)

Answer 1

ОДЗ
2x-1>0⇒x>1/2
2x-1≠1⇒x≠1
2x-3>0⇒x>3/2
2x-3≠1⇒x≠2
x∈(1,5;2) U (2;∞)
log(2x-1)(2x-3)=1/log(2x-1)(2x-3)
log²(2x-1)(2x-3)=1
1)log(2x-1)(2x-3)=-1
2x-3=1/(2x-1)
(4x²-2x-6x+3-1)/(2x-1)=0
4x²-8x+2=0
2x²-4x+1=0
D=16-8=8
x1=(4-2√2)/4=1-0,5√2 не удов усл
x2=1+0,5√2
2)log(2x-1)(2x-3)=1
2x-3=2x-1
2x-2x=1+3
0=4
нет решения