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4la puterea n +4 la puterea n+1=10×2la puterea 2009.Aflati n

Răspuns :

4^n + 4^n+1 = 10 × 2^2009

4^n × (1 + 4^1) = 10 × 2^2009

2^2n × 5 = 10 × 2^2009

2^2n = 2 × 2^2009

2^2n = 2^2010

2n = 2010

n = 2010 : 2

n = 1 005