Question

[Nguyễn Thị Gia Linh]

Tìm x

a) \(2^x.4=128\)

b) \(x^{17}=x\)

c) (2x - 2)\(^3=8\)

d) (x - 6)\(^3=\left(x-6\right)^2\)

e) (7x - 11)\(^3\) = 2\(^5\) .5\(^2\) + 200

f) 3 + 2\(^{x-1}\) = 24 - [4\(^2\) - (2\(^2\) -1)]

GIÚP MÌNH NHA!

Answer 1

[Nguyễn Đức Trí]

a) \(2^x.4=128\Rightarrow2^x=32=2^5\Rightarrow x=5\)

b) \(x^{17}=x\Rightarrow x^{17}-x=0\Rightarrow x\left(x^{16}-1\right)=0\Rightarrow x=0\) hay \(x=1\)

c) \(\left(2x-2\right)^3=8\Rightarrow\left(2x-2\right)^3=2^3\Rightarrow2x-2=2\Rightarrow2x=4\Rightarrow x=2\)

d) \(\left(x-6\right)^3=\left(x-6\right)^2\Rightarrow\left(x-6\right)^3-\left(x-6\right)^2=0\)

\(\Rightarrow\left(x-6\right)^2\left(x-6-1\right)=0\Rightarrow\Rightarrow\left(x-6\right)^2\left(x-7\right)=0\)

\(\Rightarrow x-6=0\) hay \(x-7=0\Rightarrow x=6\) hay \(x=7\)

e) \(\left(7x-11\right)^3=2^5.5^2+200\Rightarrow\left(7x-11\right)^3=32.25+200\)

\(\Rightarrow\left(7x-11\right)^3=1000=10^3\Rightarrow7x-11=10\Rightarrow7x=21\Rightarrow x=3\)

f) \(3+2^{x-1}=24-\left[4^2-\left(2^2-1\right)\right]\Rightarrow2^{x-1}=24-\left[16-3\right]-3\)

\(\Rightarrow2^{x-1}=24-13-3\Rightarrow2^{x-1}=8=2^3\Rightarrow2x-1=3\Rightarrow2x=4\Rightarrow x=2\)

Answer 2

[Nguyễn Thị Gia Linh]

Cảm ơn bạn Nguyễn Đức Trí rất nhìu nha!