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\(10^{30}=\left(10^3\right)^{10}=1000^{10}\)
\(2^{100}=\left(2^{10}\right)^{10}=1024^{10}\)
mà \(1024^{10}>1000^{10}\)
\(\Rightarrow10^{30}< 2^{100}\)
a) 1024 9 = ( 2 10 ) 9 = 2 90 < 2 100
b) 6 . 5 29 > 5 . 5 29 = 5 30
c) 10 30 = ( 10 3 ) 10 = 1000 10 ; 2 100 = ( 2 10 ) 10 = 1024 10 n ê n 10 30 < 2 100 .
a) Cách 1: 2 100 = 2 10 10 = 1024 10 > 1024 9
Cách 2: 1024 9 = 2 10 9 = 2 90 < 2 100
b) 6 . 5 29 > 5 . 5 29 = 5 30
c) 2 98 = 2 2 49 = 4 49 < 9 49
d) 10 30 = 10 3 10 = 1000 10 ; 2 100 = 2 10 10 = 1024 10 nên 10 30 < 2 100
a, Ta có 10 30 = 10 3 10 = 1000 10
2 100 = 2 10 10 = 1024 10
Vì 1000<1024 nên 1000 10 < 1024 10
Vậy 10 30 < 2 100
b, Ta có: 333 444 = 333 4 111 = 3 . 111 4 111 = 81 . 111 4 111
444 333 = 444 3 111 = 4 . 111 3 111 = 64 . 111 3 111
Vì 81 > 64 và 111 4 > 111 3 nên 81 . 111 4 111 > 64 . 111 3 111
Vậy 333 444 > 444 333
c, Ta có: 21 5 = 3 . 7 15 = 3 15 . 7 15
27 5 . 49 8 = 3 3 5 . 7 2 8 = 3 15 . 7 16
Vì 7 15 < 7 16 nên 3 15 . 7 15 < 3 15 . 7 16
Vậy 21 5 < 27 5 . 49 8
d, Ta có: 3 2 n = 3 2 n = 9 n
2 3 n = 2 3 n = 8 n
Vì 8 < 9 nên 8 n < 9 n n ∈ N *
Vậy 3 2 n > 2 3 n
e, Ta có: 2017.2018 = (2018–1).(2018+1) = 2018.2018+2018.1–1.2018–1.1
= 2018 2 - 1
Vì 2018 2 - 1 < 2018 2 nên 2017.2018< 2018 2
f, Ta có: 100 - 99 2000 = 1 2000 = 1
100 + 99 0 = 199 0 = 1
Vậy 100 - 99 2000 = 100 + 99 0
g, Ta có: 2009 10 + 2009 9 = 2009 9 . 2009 + 1
= 2010 . 2009 9
2010 10 = 2010 . 2010 9
Vì 2009 9 < 2010 9 nên 2010 . 2009 9 < 2010 . 2010 9
Vậy 2009 10 + 2009 9 < 2010 10
4. ( x - 250 ) : 6 = 64 - 12
( x- 250 ) : 6 = 52
x - 250 = 312
x = 562
5. 10x = 1030
=> x = 103
6. 30x = 120
x = 4
7. \(x=2023\)
\(8.165-\left(35:x+3\right).19=13\)
\(\left(35:x+3\right).19=152\)
\(35:x+3=8\)
\(35:x=5\)
\(x=7\)
4) \(\left(x-250\right)\div6=4^3-2^2\times3\)
\(\left(x-250\right)\div6=64-4\times3\)
\(\left(x-250\right)\div6=64-12=52\)
\(x-250=52\times6=312\)
\(x=312+250\)
\(x=562\)
5) \(2x+3x+5x=1030\)
\(x\left(2+3+5\right)=1030\)
\(10x=1030\)
\(x=1030\div10\)
\(x=103\)
6) \(15x-35x+50x=120\)
\(x\left(15-35+50\right)=120\)
\(30x=120\)
\(x=120\div30\)
\(x=4\)
7) \(\dfrac{1}{2}x+\dfrac{1}{6}x+\dfrac{1}{3}x=2023\)
\(x\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}\right)=2023\)
\(x\times1=2023\)
\(x=2023\)
8) \(165-\left(35\div x+3\right)\times19=13\)
\(\left(35\div x+3\right)\times19=165-13\)
\(\left(35\div x+3\right)\times19=152\)
\(35\div x+3=152\div19=8\)
\(35\div x=8-3=5\)
\(x=35\div5\)
\(x=7\)
a: 5^30*25=5^30*5^2=5^32<5^34
b: 16^6=(2^4)^6=2^24<2^25
c: 10^30=1000^10
4^50=(4^5)^10=1024^10
=>10^30<4^50