Question

rezolvati in multimea nr reale ecuatia 4 la puterea x-3*2la putere x+2=0

Answer 1

[tex]4^x-3*2^x+2=0 \\ (2^{2})^{x}-3*2^x+2=0\\ 2^{2x}-3*2^x+2=0\\ Notam \\ 2^{x}=t \\ t^{2}-3t+2=0 \\ \Delta=9-4*2*1=9-8=1 \\ t_1= \frac{3-1}{2}= \frac{2}{2}=1 \\ t_1= \frac{3+1}{2}= \frac{4}{2}=2 \\ 2^{x}=1 =\ \textgreater \ x_1= \log_{2} 1=0 \\ 2^{x}=2=\ \textgreater \ x_2=\log_{2} 2=1[/tex]
S={0; 1}
L-am aflat pe x conform formulei:
$a^{x}=b=\ \textgreater \ x=\log_a b$