so sánh : 64^30 và 128^25
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![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\frac{67}{77}=1-\frac{10}{77};\frac{73}{83}=1-\frac{10}{83}\)
Vì \(\frac{10}{77}>\frac{10}{83}\) nên \(1-\frac{10}{77}
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài dễ mà you ko tự suy nghĩ được, đúng là lười suy nghĩ
a) 2561=(52)61=52.61=5122
Vì 122>120 nên 5122>5120 hay 2561>5120
b) 1680 = (42)80= 42.80=4160
Vì 160>65 nên 4160>465 hay 1680>465
Mấy câu khác tự làm
![](https://rs.olm.vn/images/avt/0.png?1311)
`#3107.101107`
a)
`64^150` và `4^450`
Ta có:
`64^150 = (4^3)^150 = 4^(3*150) = 4^450`
Vì `450 = 450 => 4^450 = 4^450 => 64^150 = 4^450`
Vậy, `64^150 = 4^450`
b)
`81^64` và `27^100`
Ta có:
`81^64 = (3^4)^64 = 3^(4*64) = 3^256`
`27^100 = (3^3)^100 = 3^(3*100) = 3^300`
Vì `256 < 300 => 3^256 < 3^300 => 81^64 < 27^100`
Vậy, `81^64 < 27^100`
c)
`125^1000` và `25^3000`
Ta có:
`125^1000 = (5^3)^1000 = 5^(3*1000) = 5^3000`
Vì `5 < 25 => 5^3000 < 25^3000 => 125^1000 < 25^3000`
Vậy, `125^1000 < 25^3000`
d)
`4^30` và `3^40`
Ta có:
`4^30 = 4^(3*10) = (4^3)^10 = 64^10`
`3^40 = 3^(4*10) = (3^4)^10 = 81^10`
Vì `64 < 81 => 64^10 < 81^10 => 4^30 < 3^40`
Vậy, `4^30 < 3^40`
m)
`2^5000` và `5^2000`
Ta có:
`2^5000 = 2^(5*1000) = (2^5)^1000 = 32^1000`
`5^2000 = 5^(2*1000) = (5^2)^1000 = 25^1000`
Vì `32 > 25 => 32^1000 > 25^1000 => 2^5000 > 5^2000`
Vậy, `2^5000 > 5^2000`
h)
`6^450` và `3^750`
Ta có:
`6^450 = 6^(150*3) = (6^3)^150 = 216^150`
`3^750 = 3^(150*5) = (3^5)^150 = 243^150`
Vì `216 < 243 => 216^150 < 243^150 => 6^450 < 3^750`
Vậy, `6^450 < 3^750`
0)
`333^444` và `444^333`
Ta có:
`333^444 = 333^(4*111) = (333^4)^111 = (3^4 *111^4)^111 = 81^111 * 111^444`
`444^333 = 444^(3*111) = (444^3)^111 = (4^3 * 111^3)^111 = 64^111 * 111^333`
Vì `81 > 64;` `111^444 > 111^333`
`=> 81^111 * 111^444 > 64^111 * 111^333`
Vậy, `333^444 > 444^333.`
a) Ta có:
\(64^{150}=\left(2^6\right)^{150}=2^{900}\)
\(4^{450}=\left(2^2\right)^{450}=2^{900}\)
Mà: \(2^{900}=2^{900}\Rightarrow64^{150}=4^{450}\)
b) Ta có:
\(81^{64}=\left(3^4\right)^{64}=3^{256}\)
\(27^{100}=\left(3^3\right)^{100}=3^{300}\)
Mà: \(3^{300}>3^{256}\Rightarrow27^{100}>81^{64}\)
c) Ta có:
\(125^{1000}=\left(5^3\right)^{1000}=5^{3000}\)
Mà: \(25^{3000}>5^{3000}\Rightarrow25^{3000}>125^{1000}\)
d) Ta có:
\(4^{30}=\left(4^3\right)^{10}=64^{10}\)
\(3^{40}=\left(3^4\right)^{10}=81^{10}\)
Mà: \(81^{10}>64^{10}\Rightarrow3^{40}>4^{30}\)
m) Ta có:
\(2^{5000}=\left(2^5\right)^{1000}=32^{1000}\)
\(5^{2000}=\left(5^2\right)^{1000}=25^{1000}\)
Mà: \(25^{1000}< 32^{1000}\Rightarrow2^{5000}>5^{2000}\)
h) Ta có:
\(6^{450}=\left(6^3\right)^{150}=216^{150}\)
\(3^{750}=\left(3^5\right)^{150}=243^{150}\)
Mà: \(243^{150}>216^{150}\Rightarrow3^{750}>6^{450}\)
....
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Ta có :
\(27^{27}>27^{26}=\left(27^2\right)^{13}=729^{13}>243^{13}\)
\(\Rightarrow27^{27}>243^{13}\)
\(\Rightarrow-27^{27}< -243^{13}\)
\(\Rightarrow\left(-27\right)^{27}< \left(-243\right)^{13}\)
b) \(\left(\dfrac{1}{8}\right)^{25}>\left(\dfrac{1}{8}\right)^{26}=\left(\dfrac{1}{8^2}\right)^{13}=\left(\dfrac{1}{64}\right)^{13}>\left(\dfrac{1}{128}\right)^{13}\)
\(\Rightarrow\left(\dfrac{1}{8}\right)^{25}>\left(\dfrac{1}{128}\right)^{13}\)
\(\Rightarrow\left(-\dfrac{1}{8}\right)^{25}< \left(-\dfrac{1}{128}\right)^{13}\)
c) \(4^{50}=\left(4^5\right)^{10}=1024^{10}\)
\(8^{30}=\left(8^3\right)^{10}=512^{10}< 1024^{10}\)
\(\Rightarrow4^{50}>8^{30}\)
d) \(\left(\dfrac{1}{9}\right)^{17}< \left(\dfrac{1}{9}\right)^{12}< \left(\dfrac{1}{27}\right)^{12}\)
\(\Rightarrow\left(\dfrac{1}{9}\right)^{17}< \left(\dfrac{1}{27}\right)^{12}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(S=4\cdot\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\cdot...\cdot\left(3^{64}+1\right)\)
\(\left(3^2-1\right)S=4\cdot\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\cdot...\cdot\left(3^{64}+1\right)\)
\(8S=4\cdot\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\cdot...\cdot\left(3^{64}+1\right)\)
\(2S=\left(3^8-1\right)\left(3^8+1\right)\cdot...\cdot\left(3^{64}+1\right)\)
...
\(2S=3^{128}-1\)
Vậy S < 3128 - 1
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{16}-\frac{1}{32}-\frac{1}{64}-\frac{1}{128}\)
\(=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\right)-2\times\left(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\right)\)
\(=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{16}-\frac{1}{32}-\frac{1}{64}\)
\(=\frac{1}{128}\)< 1
còn 1 cách nữa mk lm nhưng ko chắc nên hỏi
1/2-(1/4+1/8+1/32+1/64+1/128)
=1/2-(1/2-1/4+1/4-1/8+1/8-1/32+1/32-1/64+1/64-1/128)
=1/2-(1/2-1/128)
=1/2-63/128
=1/128
![](https://rs.olm.vn/images/avt/0.png?1311)