Interesting logarithm equation

[Math Tutor]

Here is an interesting logarithm equation:
[tex]10^{lg^2x-3}+x(lg^2x-2lgx-3)=x^2[/tex]

[ivan9302]

[tex]lgx=a[/tex] and
[tex]10^{a^2-3}+10^2a(a^2-2a-3)=10^2a[/tex] [tex]/ 10^2a[/tex] and

[tex]10^{a^2-2a-3}+\frac{a^2-2a-3}{ 10^a} =1[/tex]

[tex]a^2-2a-3=y[/tex] and
[tex]10^y+\frac{y}{ 10^a}=1[/tex] it is true when y=0
and now [tex]a^2-2a-3=0[/tex]
[tex]a_1=3, a_2=-1[/tex]

[tex]lx=10^a[/tex]

[tex]x=1000[/tex], [tex]x=0.1[/tex]