Bài tập: Tìm số nguyên x, biết:
1. (1/3+1/6) 2^x + 2^x+1=2^12 + 2^10
2. (1/3+1/6) 2^x+4 – 2^x = 2^13 – 2^10
Bài tập: Tìm số nguyên x, biết: 1. (1/3+1/6) 2^x + 2^x+1=2^12 + 2^10 2. (1/3+1/6) 2^x+4 – 2^x = 2^13 – 2^10
By Maria
By Maria
Bài tập: Tìm số nguyên x, biết:
1. (1/3+1/6) 2^x + 2^x+1=2^12 + 2^10
2. (1/3+1/6) 2^x+4 – 2^x = 2^13 – 2^10
`1,(1/3 + 1/6) . 2^x + 2^(x + 1) = 2^12 + 2^10`
`⇔ 1/2 . 2^x + 2^x . 2 = 2^12 + 2^10`
`⇔ 2^x (1/2 + 2) = 2^10(2^2 + 1)`
`⇔ 2^x . 5/2 = 5120`
`⇔ 2^x = 5120 : 5/2 `
`⇔ 2^x = 2048`
`⇔ 2^x = 2^11`
`⇔ x = 11`
`2,(1/3 + 1/6) . 2^(x + 4) – 2^x = 2^13 – 2^10`
`⇔ 1/2 . 2^x . 2^4 – 2^x . 1 = 2^10 . 7`
`⇔ (8 – 1).2^x = 2^10. 7`
`⇔7 . 2^x = 2^10. 7`
`⇔ 2^x = 2^10`
`⇔ x = 10`
Xin hay nhất !
Đáp án:
a) x = 11
b) x = 10
Giải thích các bước giải:
1. (1/3 + 1/6) . 2^x + 2^(x + 1) = 2^12 + 2^10
=> 1/2 . 2^x + 2^x . 2 = 2^12 + 2^10
=> 2^x (1/2 + 2) = 2^10(2^2 + 1)
=> 2^x . 5/2 = 2^10 . 5
=> 2^x . 5/2 = 5120
=> 2^x = 5120 : 5/2 = 5120.2/5 = 2048
=> 2^x = 2^11
=> x = 11
2. (1/3 + 1/6) . 2^(x + 4) – 2^x = 2^13 – 2^10
=> 1/2 . 2^x . 2^4 – 2^x . 1 = 2^10 . 7
=> 8 . 2^x – 2^x . 1 = 2^10. 7
=> (8 – 1).2^x = 2^10.7
=> 7 . 2^x = 2^10.7
=> x = 10