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a/ 777333 = [(7 . 111)3]111 = (73 . 1113)111
333777 = [(3 . 111)7]111 = (37 . 1117)111
Do: 37 > 73 ; 1117 > 1113 => (37 . 1117)111 > (73 . 1113)111
=> 333777 > 777333
(111 + 222 + 333 + 444 + 555 + 666 + 777 + 888 + 999)x 2.................999 x 2 x 2 x 2 ?
A.(111 + 222 + 333 + 444 + 555 + 666 + 777 + 888 + 999)x 2 > 999 x 2 x 2 x 2 = 9990 > 7992
B.(111 + 222 + 333 + 444 + 555 + 666 + 777 + 888 + 999)x 2 < 999 x 2 x 2 x 2 = 9990 < 7992
C.(111 + 222 + 333 + 444 + 555 + 666 + 777 + 888 + 999)x 2 = 999 x 2 x 2 x 2 = 9990 = 7992
a , \(2^{3000}=\left(2^3\right)^{1000}=8^{1000}\)
\(3^{2000}=\left(3^2\right)^{1000}=9^{1000}\)
Mà \(8^{1000}< 9^{1000}\)
\(\Rightarrow2^{3000}< 3^{2000}\)
b , \(777^{333}=\left(777^3\right)^{111}=\text{469097433}^{111}\)
\(333^{777}=\left(333^7\right)^{111}=\text{36926037}^{111}\)
Mà 469097433111>36926037111
=> 777333>333777
23000=(23)1000 =81000và 32000=(32)1000 =91000
Vì 8 < 9 nên 81000 < 91000
do đó 23000 <32000
777333=(7773)111
333777=(3337)111
Vì 7773<3337 nên 777333<333777
Chắc chắn đúng đấy . Nhấn nút cảm ơn đi nhé
có \(777^{333}=\left(7.111\right)^{333}=7^{333}.111^{333}=7^{3.111}.111^{333}=\left(7^3\right)^{111}.111^{333}=343^{111}.111^{333}\)
mà \(333^{777}=\left(3.111\right)^{777}=3^{777}.111^{777}=\left(3^7\right)^{111}.111^{777}=2187^{111}.111^{777}\)
ta thấy \(343^{111}< 2187^{111},111^{333}< 111^{777}\)
=> \(343^{111}.111^{333}< 2187^{111}.111^{777}\)=> \(333^{777}< 777^{333}\)
vậy...
\(777^{333}=7^{333}.111^{333}=\left(7^3\right)^{111}.111^{333}=343^{111}.111^{333}\)
\(333^{777}=3^{777}.111^{777}=\left(3^7\right)^{111}.111^{777}=2187^{111}.111^{777}\)
Vì \(343^{111}< 2187^{111};111^{333}< 111^{777}\Rightarrow777^{333}< 333^{777}\)
Ta có: \(777^{333}=\left(777^3\right)^{111}=\left[\left(7.111\right)^3\right]^{111}=\left[7^3.111^3\right]^{111}\)
\(=\left[343.111^3\right]^{111}\)
\(333^{777}=\left(333^7\right)^{111}=\left[\left(3.111\right)^7\right]^{111}=\left[3^7.111^7\right]^{111}=\left(2187.111^7\right)^{111}\)
Vì \(343.111^3< 2187.111^7\Rightarrow777^3< 333^7\)
Ta có: 777333 = 777(3.111) = (7773)111 = 2331111
333777 = 333(7.111) = (3337)111 = 2331111
=> 2331 = 2331 mà 2331111 = 2331111 hay 777333 = 333777
Bài 1:
a)Ta có:
2300=(23)100=8100
3200=(32)100=9100
Vì 8100<9100 => 2300<3200
b)Ta có:
777333=(7*111)333=7333*111333
=(73)111*111333=343*111333
333777=(111*3)777=111777*3777
=111777*(37)111=2187*111777
Vì 343*111333<2187*111777 =>777333<333777
\(x\) là dấu x nha