Pomogite pojalusyta. Nayti proizvedeniye korney. x^lgx=1000x^2

Question

Pomogite pojalusyta. Nayti proizvedeniye korney. x^lgx=1000x^2

Answer 1

X^lg(x)=1000x^2
ОДЗ: x>0
logx(1000x^2)=lg(x)
logx(10^3)+logx(x^2)=lg(x)
3logx(10)+2=lg(x)
3/lg(x)+2=lg(x)
lg(x)=t
3/t+2=t
t^2-2t-3=0
t1=-1
t2=3
lg(x)=-1
x=1/10
lg(x)=3
x=1000

Comments

Наверно правильно

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