Đáp án:
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Giải thích các bước giải:
`3`.
a) Ta có:
`5<11` và `16<24`
`=>5^16<11^24`
Vậy `5^16<11^24`.
b) `3^(2n)=(3^2)^n=9^n`
`2^(3n)=(2^3)^n=8^n`
`=>9^n>8^n=>3^(2n)>2^(3n)`
Vậy `3^(2n)>2^(3n`.
c) `6. 5^22=(5+1).5^22=5^23+5^22>5^23`
`=>6. 5^22>5^23`
Vậy `6. 5^22>5^23`.
d) `2^16=2^(13+3)=2^13. 2^3`
`=>2^13. 2^3>2^13`
`=>2^16>2^13`
Vậy `2^13<2^16`.
e) `27^5. 49^8`
`=(3^3)^5. (7^2)^8`
`=3^15. 7^16`
`=3^15. 7^15. 7`
`=21^15. 7>21^15`
`=>21^15<27^3. 49^8`
Vậy `21^15<27^3. 49^8`.
f) `72^45-72^44`
`=72^44.(72-1)`
`=72^44. 71`
`72^44-72^43`
`=72^43.(72-1)`
`=72^43. 71`
`=>72^44. 71>72^43 .71`
`=>72^45-72^44>72^44-72^43`
Vậy `72^45-72^44>72^44-72^43`.
`4`.
a) Dãy số có $(x-1):2+1=\dfrac{x+1}{2}$ số hạng.
$1+3+5\,+\,.\!.\!.+\,x=1600\\\Rightarrow \dfrac{(x+1)\cdot\dfrac{x+1}{2}}{2}=1600\\\Rightarrow \dfrac{(x+1)^2}{4}=1600\\\Rightarrow (x+1)^2=6400\\\Rightarrow (x+1)^2=80^2\\\Rightarrow x+1=80\\\Rightarrow x=79$
Vậy `x=79`.
b) `2^x+2^(x+3)=144`
`=>2^x.(1+2^3)=144`
`=>2^x. 9=144`
`=>2^x=16`
`=>2^x=2^4`
`=>x=4`
Vậy `x=4`.
