Đáp án+Giải thích các bước giải:

Bài `8:`

`a)`

`(x-1)^3=125`

`(x-1)^3=5^3`

`x-1=5`

`x=6`

`b)`

`2^(x+2)-2^x=96`

`2^x. 2^2-2^x=96`

`2^x.(2^2-1)=96`

`2^x.3=96`

`2^x=32`

`2^x=2^5`

`x=5`

`c)`

`(2x+1)^3=343`

`(2x+1)^3=7^3`

`2x+1=7`

`2x=6`

`x=3`

`d)`

`720:[41-(2x-5)]=2^3.5`

`720:[41-(2x+5)]=40`

`41-(2x+5)=720:40`

`41-(2x+5)=18`

`2x+5=23`

`2x=18`

`x=9`

`e)`

`16^x<128^4`

`(2^4)^x<(2^7)^4`

`2^4x< 2^(7.4)`

`x<7`

`x∈{0;1;2;3;4....;6}`

Bài `9:`

`A=2+2^2+.......+2^100`

`2A=2^2+2^3+...........+2^101`

`2A-A=(2^2+2^3+...........+2^101)-(2+2^2+.......+2^100)`

`A=2^101-2`

`B=1+3+3^3+............+3^2009`

`3B=3+3^2+3^3+.............+3^2010`

`3B-B=(3+3^2+3^3+.............+3^20100-(1+3+3^2+..........+3^2009)`

`2B=3^2010-1`

`B=(3^2010-1)/2`

`C=1+5+5^2+...........+5^1998`

`5C=5+5^2+5^3+............+5^1999`

`5C-C=(5+5^2+............+5^1999)-(1+5+5^2+.......+5^1998)`

`4C=5^1999-1`

`C=(5^1999-1)/4`

`D=4+4^2+4^3+.........+4^n`

`4D=4^2+4^3+..........+4^(n+1)`

`3D=4^(n+1)-4`

`D=(4^(n+1)-4)/4`

Bài `10`:

`A=1+2+2^2+...........+2^100`

`2A=2+2^2+............+2^101`

`2A-A=2^101-1`

`A=2^101-1`

`A+1=2^101`

Bài `11:`

`B=3+3^2+..........+3^2005`

`3B=3^2+3^3+..............+2^2006`

`2B=3^2006-3`

`2B+3=3^2006`