`2^x + 2^(x + 1) + 2^(x + 2) + 2^(x + 3) + ... + 2^(x + 2015) = 2^2019 - 8`
`2^x . 2^0 + 2^x . 2^1 + 2^x . 2^2 + 2^x . 2^3 + ... 2^x . 2^2015 = 2^2019 - 8`
`2^x . (2^0 + 2^1 + 2^2 + 2^3 + ... + 2^2015) = 2^2019 - 8`
`Đặt:`
`A = 2^0 + 2^1 + 2^2 + 2^3 + ... + 2^2015`
`2A = 2^1 + 2^2 + 2^3 + ... + 2^2016`
`2A - A = (2^1 + 2^2 + 2^3 + ... + 2^2016) - (2^0 + 2^1 + 2^2 + 2^3 + ... + 2^2015)`
`A = 2^2016 - 2^0`
`A = 2^2016 - 1`
`2^x . (2^2016 - 1) = 2^2019 - 8`
`2^x = (2^2019 - 8)/(2^2016 - 1) = (2^2019 - 2^3)/(2^2016 - 1) = (2^3 . (2^2016 - 1))/(2^2016 - 1) = 2^3`
`⇒ x = 3`
