Question

2 la ×-1 + 2 la × = 12 sa se determine solutiile reale ale ecuatiei

Answer 1

[tex]2^{x-1}+2^{x}=12\\Notam: 2^{x}=t\\\frac{t}{2}+t=12\\\frac{t}{2}+\frac{2t}{2}=12\\ 3t=12*2\\3t=24\\t=\frac{24}{3}\\t=8\\2^{x}=8\\2^{x}=2^{3}\\x=3[/tex]

Answer 2

2^(x-1)+2^x=12 ⇔ 2^(x-1)(1+2) =12 ⇔2^(x-1)·3=12 |:3 ⇔ 2^(x-1) = 4

⇔ 2^(x-1) = 2^2 ⇔ x-1 =2 ⇔ x= 3