Đáp án:

Giải thích các bước giải:

`3)`

`a)3<3^n<=243=3^5`

`=>3^1<3^n<=3^5`

`=>n in {2;3;4;5}`

`b)8*16>= 2^n >=4`

`=>8*16=2^3*2^4=2^7>=2^n>=2^2`

`=>n in {7;6;5;4;3;2}`

`c)125*5>=5^n>=5`

`=>5^3*5=5^4>=5^n>=5^1`

`=> n in {4;3;2;1}`

`d)5^n+5^(n+2)=650`

`=>5^n(1+5^2)=650`

`=>5^n*26=650`

`5^n=25=5^2`

`=>n=2`

`4)`

`a)x^2=4x^4`

`=>4x^4-x^2=0`

`=>x^2(4x^2-1)=0`

`=>`$\left[\begin{matrix} x^2=0\\ 4x^2-1=0\end{matrix}\right.$

`=>`$\left[\begin{matrix}x=0\\\left[\begin{matrix}x=1/2\\x=-1/2\end{matrix}\right.\end{matrix}\right.$

` Vậy  x in {0;1/2;-1/2}`

`b)2x-1=(2x-1)^3`

`=>(2x-1)^3-(2x-1)=0`

`=>(2x-1)*[(2x-1)^2-1]=0`

`=>`$\left[\begin{matrix}2x-1=0\\ (2x-2)^2-1=0\end{matrix}\right.$

`=>$\left[\begin{matrix} x=1/2\\ (2x-1)^2=1\end{matrix}\right.$

`=>`$\left[\begin{matrix} x=1/2\\ \left[\begin{matrix} x=1\\ x=0\end{matrix}\right.\end{matrix}\right.$

` Vậy  x  in {1/2;1;0}`

`c)(x-3)^(2x)=(x-3)^(2x+1)`

`=>(x-3)^(2x+1)-(x-3)^(2x)=0`

`=>(x+3)^(2x)*[(x-3)-1]=0`

`=>`$\left[\begin{matrix} (x+3)^(2x)=0\\ (x-3)-1=0\end{matrix}\right.$

`=>`$\left[\begin{matrix}x=-3\\ x=4\end{matrix}\right.$

` Vậy  x in {-3;4}`

`d)(8x-1)^(2x+1)=5^(2x+1)`

`=>8x-1=5`

`=>8x=6`

`=>x=3/4`

` Vậy x=3/4`

` Ngochoa#~~`