[tex] lg^{4}x- lg^{2}x=12[/tex]
Conditii de existenta: x>0
Notezi lg^{2}x = (lg x)^2=t, t>0
t²-t=12
t²-t-12=0
Δ=1²- 4*1*(-12)=1+48=49
√Δ=7
t1=1+7 = 4
2
t2= 1-7 = -3 , t>0 deci -3 nu este solutie
2
Pt t=4 => lg^{2}x = 4 => (lg x)^2=4 =>| lgx| = 2=> lgx=+ 2 sau -2=>
[tex]log_{10}x [/tex]=2=> x=10²=100
[tex]log_{10}x [/tex]= - 2 => x=[tex] \frac{1}{ 10^{2} } = \frac{1}{100} [/tex]
