2.2ˣ = 64

2ˣ = 64 : 2

2ˣ = 32

2ˣ = 2⁵

x = 5

cách 1

2^x-2.2³=64

2^x-2.2³=2⁶

2^x-2+3=2⁶

=>x-2+3=6

x-2=6-3

x-2=3

x=3+2

x=5

cách 2

2^x-2.2³=64

2^x-2.8=64

2^x-2=64:8

2^x-2=8

2^x-2=2³

=>x-2=3

x=2+3

x=5

ko phải đâu cái ^x-2 là mũ của 2

Xét khai triển:

\(\left(1+2x\right)^{2n+1}=C_{2n+1}^0+C_{2n+1}^1.2x+C_{2n+1}^2\left(2x\right)^2+...+C_{2n+1}^{2n+1}\left(2x\right)^{2n+1}\)

Đạo hàm 2 vế:

\(2\left(2n+1\right)\left(1+2x\right)^{2n}=2C_{2n+1}^1+2^2C_{2n+1}^2x+...+\left(2n+1\right)2^{2n+1}C_{2n+1}^{2n+1}x^{2n}\)

\(\Leftrightarrow\left(2n+1\right)\left(1+2x\right)^{2n}=C_{2n+1}^1+2C_{2n+1}^2x+...+\left(2n+1\right)2^{2n}C_{2n+1}^{2n+1}x^{2n}\)

Cho \(x=-1\) ta được:

\(2n+1=C_{2n+1}^1-2C_{2n+1}^2+...+\left(2n+1\right)2^{2n}C_{2n+1}^{2n+1}\)

\(\Rightarrow2n+1=2019\Rightarrow n=1009\)