Question

2 la puteria 2010 + 4 la puteria 1005 + 8 la puteria 670 = 3×2 la puteria 5n . Aflatil pe n

Answer 1

      
[tex]2^{2010}+4^{1005}+8^{670}=3 \times 2^{5n} \\ 2^{2010}+(2^2)^{1005}+(2^3)^{670}=3 \times 2^{5n} \\ 2^{2010}+2^{2 \times 1005}+2^{3 \times 670}=3 \times 2^{5n} \\ 2^{2010}+2^{2010}+2^{2010}=3 \times 2^{5n} \\ 3 \times 2^{2010}=3 \times 2^{5n} ~~~~~~~| : 3 \\ 2^{2010}=2^{5n} \\ \Longrightarrow ~5n = 2010 \\ \\ \displaystyle n= \frac{2010}{5} = \boxed{402}[/tex]

Answer 2

2 la puterea 2010+4 la puterea 1005+8 la puterea 670=3*2 la puterea 5n
2 la puterea 2010+2 la puterea 2*1005+2 la puterea 3*670=3*2 la puterea 5n
2 la puterea 2010+2 la puterea 2010+2 la puterea 2010=3*2 la puterea 5n
3*2 la puterea 2010=3*2 la puterea 5n       /:3
2 la puterea 2010=2 la puterea 5n
5n = 2010
n=402
Sper ca tiam fost de ajutor  !!!!!!!!!!!!!!!!!!!!!!!