Câu `11:`

`a)(x-1)^2=9`

`(x-1)^2 =3^2` hoặc `(-3)^2`

`x-1=(+-3)`

`th_1:x-1=3`

`x=4`

`th_2:x-1=-3`

`x=-2`

Vậy: `x in {4;-2}`

``

`b)(x-1)^3=-0,001`

`(x-1)^3 =(-0,1)^3`

`x-1=-0,1`

`x=9/10`

Vậy: `x=9/10`

``

`c)(3x-1)^2=81`

`(3x-1)^2 =9^2` hoặc `(-9)^2`

`3x-1=(+-9)`

`th_1:3x-1=9`

`3x=10`

`x=10/3`

`th_2:3x-1=-9`

`3x=-8`

`x=-8/3`

Vậy: `x in {10/3;-8/3}`

``

`d)(2x+1)^3=-0,001`

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

`2x+1=-0,1`

`2x=-11/10`

`x=-11/20`

Vậy: `x=-11/20`

``

Câu `12:`

`a)2^(2x-1)=32`

`2^(2x-1)=2^5`

`2x-1=5`

`2x=6`

`x=3`

Vậy: `x=3`

``

`b)5^(x+1)=125`

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

`x+1=3`

`x=2`

Vậy: `x=2`

``

Câu `13:`

`a)3^200=(3^2)^100=9^100`

`2^300=(2^3)^100=8^100`

Vì: `9 > 8 =>9^100 > 8^100`

Vậy: `3^200 > 2^300`

``

`b)8^12=(8^3)^4=512^4`

`12^8=(12^2)^4=144^4`

Vì: `512>144=>512^4 > 144^4`

Vậy: `8^12 > 12^8`

``

Câu `14:`

`16/81=(4^2)/(9^2)=(4/9)^2`

`(-125)/216=((-5)^3)/(6^3)=((-5)/6)^3`

``

Câu `16`

`a)32<2^n<128`

`2^5 < 2^n < 2^7`

`5<n<7`

`=>n=6`

Vậy: `n=6`

``

`b)2*16≥2^n>4`

`2*2^4 ≥ 2^n > 2^2`

`2^5 ≥2^n > 2^2`

`5≥n>2`

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

Vậy: `n in {5;4;3}`

``

Câu `17:`

`a)(-32)^9=[(-2)^5]^9=(-2)^45`

`(-16)^13 =[(-2)^4]^13=(-2)^52`

Vì: `45 < 52 => (-2)^45 > (-2)^52`

Vậy: `(-32)^9 > (-16)^13`

``

`b)(-5)^30 =[(-5)^3]^10 = (-125)^10`

`(-3)^50 =[(-3)^5]^10=(-243)^10`

Vì: `-125 > -243 => (-125)^10 > (-243)^10`

Vậy: `(-5)/30 > (-3)/50`

``

`a)1/(2^300)=[(1/2)^3]^100=(1/8)^100`

`1/(3^200)=[(1/3)^2]^100=(1/9)^100`

Vì: `1/8> 1/9 => (1/8)^100 > (1/9)^100`

Vậy: `1/(2^300)>1/(3^200)`

``

`b)` Ta có:

`5^199 < 5^200 =(5^2)^100 =25^100`

`3^300 =(3^3)^100 =27^100`

Vì: `25^100 < 27^100 => 5^199 < 3^300`

Vì Vậy: `1/(5^199) > 1/(3^300)`

``

Câu `19`

`a)5^20=(5^2)^10 =25^10`

`3^34 > 3^30 =(3^3)^10 =27^10`

Vì: `25^10 < 27^10 => 5^20 < 3^30`

Vậy: `5^20 < 3^34`

``

`b)(-5)^39 =[(-5)^3]^13 =(-125)^13`

`(-2)^91 =[(-2)^7]^13 =(-128)^13`

Vì: `-125 > -128 => (-125)^13 > (-128)^13`

Vạy: `(-5)^39 > (-2)^91`