Question

решите логарифм

2lgx/lg(4x-3)=1

Answer 1

2lgx/lg(4x-3)=1
log_{4x-3} (x²)=1
x²=4x-3
x²-4x+3=(x-1)(x-3)=0
x=1, x=3
4x-3>0
x>3/4
4x-3≠1
x≠3/4
x>0
Отв: x=1, x=3

Answer 2

ОДЗ x>0 u 4x-3>0⇒x>3/4⇒x∈(3/4;∞)
2lgx=lg(4x-3)
lgx²-lg(4x-3)=0
lgx²/(4x-3)=0
x²/(4x-3)=1
x²-4x+3=0
x1+x2=4 U x1*x2=3
x1=1 U x2=3