1) CE: x²>0,x>0
[tex]log_{ \frac{1}{2} }x^{2}-log_{ \frac{1}{2} } x=lg4+lg25 \\ log_{ \frac{1}{2} } x=lg100 \\ log_{ \frac{1}{2} } x=2 [/tex]
[tex]x=( \frac{1}{2})^{2} = \frac{1}{4} [/tex]
conditiile de existenta sunt indeplinite,deci Sol: {1/4}
2)CE: x+2>0=> x>-2.
notez log₃(x+2)=t.
ecuatia devine t²-3t-4=0
Δ=9+16=25
t₁=4
t₂=-1.
pt t=4 log₃(x+2)=4; 3⁴=x+2; x+2=81 => x=79.
pt t=-1 log₃(x+2)=-1; 3⁻¹=x+2; x+2=1/3 => x=-5/3
conditiile sunt indeplinite,deci Sol: {-5/3 ; 79}
3) CE: x>0.
notez lg x=t
12-t²=t
t²+t-12=0.
Δ=1+48=49.
t₁=4
t₂=-3.
pt t=4 lg x=4; x=10⁴=10000.
pt t=-3 lg x=-3; x=10⁻³=1/1000
conditiile sunt indeplinite ,deci Sol: {1/1000; 10000}
