\(2.\)
\(a.\)
Ta có : \(2^{332}< 2^{333}=\left(2^3\right)^{111}=8^{111}\)
\(3^{223}>3^{222}=\left(3^2\right)^{111}=9^{111}\)
Vì \(8^{111}< 9^{111}\)
\(\Rightarrow2^{332}< 3^{223}\)
\(b.\)
Ta có : \(90^{20}=\left(9^2\right)^{10}=81^{10}\)
Vì \(81^{10}< \) \(9999^{10}\)
\(\Rightarrow99^{20}< 9999^{10}\)
\(3.\)
\(a.\)
Ta có : \(\left(2x+1\right)^2=4\)
\(\Rightarrow2x+1=\pm\sqrt{4}=\pm2\)
\(\Rightarrow\left[{}\begin{matrix}2x+1=2\\2x+1=-2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=-\dfrac{1}{2}\end{matrix}\right.\)
\(b.\)
\(\left(3x-1\right)^3=27\)
\(\Rightarrow\left(3x-1\right)^3=3^3\)
\(\Rightarrow3x-1=3\)
\(\Rightarrow x=\dfrac{4}{3}\)
\(c.\)
\(\left(3x-1\right)^3=-\dfrac{8}{27}\)
\(\Rightarrow\left(3x-1\right)^3=\left(-\dfrac{2}{3}\right)^3\)
\(\Rightarrow3x-1=-\dfrac{2}{3}\)
\(\Rightarrow x=\dfrac{1}{9}\)
1 a) 2.16>2n>4 => 25>2n>22 => 5>n>2 => n=3;4
b) 9.27<3n<243 => 33<3n<35 => 3<n<5 => n=4
c) 125>5n+1>25 => 53>5n+1>52 =>3>n+1>2 => 3-1>n+1-1>2-1
=> 2>n>1 => không có giá trị nào của n để 2>n>1 khi n là số tự nhiên
2 a) 2332<2333 mà 2333=23.111=8111
3223>3222 mà 3222=32.111=9111
Vì 8111<9111 => 2333<3222 => 2332<3233
b) 9920=992.10=980110 mà 980110<999910 nên 9920<999910
3 a) (2x+1)2=4=22 => 2x+1=2 => x=\(\dfrac{1}{2}\)
b) (3x-1)3=27=33 => 3x-1=3 => x=\(\dfrac{4}{3}\)
c) (3x-1)3=-8/27=(-2/3)3 => 3x-1=-2/3 => x=\(\dfrac{1}{9}\)