Question

Решите уравнение
log5 (√3x+4)*log(x) 5 =1

Answer 1

ОДЗ
3x+4>0⇒x>-4/3 U x>0 U x≠1
x∈(0;1) U(1;∞)
log(5)√(3x+4)*1/log(5)x=1
log(5)√(3x+4) = log(5)x
log(5)√(3x+4)-log(5)x=0
log(5)√(3x+4)/x=0
√(3x+4)/x=1
√(3x+4)=x
3x+4=x²
x²-3x-4=0
x1+x2=3 U x1*x2=-4
x1=-1∉ОДЗ
x2=4