`(`*`)`
Ta có: `M = 2 + 2^2 + 2^3 + ... + 2^20`
`= (2 + 2^2 + 2^3 + 2^4) + ... + (2^17 + 2^18 + 2^19 + 2^20)`
`= 2(1 + 2 + 2^2 + 2^3) + ... + 2^17(1 + 2 + 2^2 + 2^3)`
`= 2 . 15 + ... + 2^17 . 15`
`= 15(2 + ... + 2^17) = 5 . 3 . (2 + ... + 2^17) \vdots 5`
`⇒ đpcm`
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`(`**`)`
`5 . 4^x + 4^(x + 1) = 9 . 4^5`
`⇒ 5 . 4^x + 4^x . 4 = 9 . 4^5`
`⇒ 4^x . (5 + 4) = 9 . 4^5`
`⇒ 4^x . 9 = 9 . 4^5`
`⇒ x = 5`
Vậy `x = 5`
