Question

rezolvati in multimea numerelor reale ecuatia 2x2(la puterea x)=4(la puterea x-2)

Answer 1

2^(x+1)=2^(2x-4)
2x-4=x+1
x=5


verificare
2*32=4³
64=64, adevarat , bine rezolvat



Obs:
am tinut cont ca 2*2^x= 2^1*2^x
si ca
4*(x-2) =(2²)^(x-2)

Answer 2

[tex]\it 2\cdot2^x = 4^{x-2} \Leftrightarrow 2^{x+1} = (2^2)^{x-2} \Leftrightarrow 2^{x+1} = 2^{2x-4} \Leftrightarrow \\ \\ \Leftrightarrow x+1=2x-4 \Leftrightarrow 1+4=2x-x \Leftrightarrow 5=x\Leftrightarrow x=5[/tex]