Răspuns:
3*9ˣ+2*12ˣ=16ˣ
2*(3²ˣ)+2*3ˣ*4ˣ=4²ˣ
Impari egalitatea prin 3²ˣ
2(3²ˣ/3²ˣ)+2(3ˣ/3ˣ)*(4ˣ/3x)=4²ˣ/3²ˣ
2*1+2*1*(4/3)ˣ=(4/3)²ˣ
2+2*(4/3)ˣ=(4/3)²ˣ
Substitutie
(4/3)ˣ =y y>0
2+2y=y²
y²-2y-2=0
Δ=4+8=12
y1=(2-√12)/2=(2-2√3)/2=1-√3<0 Nu convine ecuatiei
y2=1+√3 >0 se accepta
2/3ˣ=1+[tex]\sqrt{3}[/tex]
x=log(2/3)(1+√3)
Explicație pas cu pas:
x=
