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2^70 va 3^51
vi 3^51>3^50 ma 3^50=(3^5)^10=243^10
2^70=(2^7)10=128^10
=>3^50>2^70
vi 3^51>3^50 nen 3^51>2^70
cau tiep theo lam tuong tu nhe!
(xin loi may tinh cua minh khong danh duoc dau)
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Vì 2017<2018 nên\(\frac{1}{2017}\)>\(\frac{1}{2018}\)
⇒\(\frac{2}{2017}\)>\(\frac{1}{2018}\)
⇒\(\frac{2015}{2017}\)=1-\(\frac{2}{2017}\)<1-\(\frac{1}{2018}\)=\(\frac{2017}{2018}\)
Vậy, \(\frac{2015}{2017}\)< \(\frac{2017}{2018}\)
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20^1000=(20^10)^100;20^900=(20^9)^100
=>20^10>20^9
=>20^1000>20^900
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Ta có công thức sau: \(\frac{a}{b}\) > \(\frac{a+m}{b+m}\) ( m khác 0;\(\frac{a}{b}\)>1)
Vì 20^10-1>20^10-3 => B>1
Áp dụng vào bài giải ta có:
A=\(\frac{\left(20^{10}-1\right)+2}{\left(20^{10}-3\right)+2}\) < \(\frac{20^{10}-1}{20^{10}-3}\)= B
Vậy A < B
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Ta có
\(2^{30}=\left(2^3\right)^{10}=8^{10}\)
\(3^{20}=\left(3^2\right)^{10}=9^{10}\)
Vì 8 < 9 hay \(8^{10}< 9^{10}\)nên \(2^{30}< 3^{20}\)
Ta có:
\(2^{30}=\left(2^3\right)^{10}=8^{10}\)
\(3^{20}=\left(3^2\right)^{10}=9^{10}\)
Vì 8 < 9 \(\Rightarrow8^{10}< 9^{10}\)
\(\Rightarrow2^{30}< 3^{20}\)
Ta có :
\(2^{70}=\left(2^7\right)^{10}=128^{10}\)
\(7^{20}=\left(7^2\right)^{10}=49^{10}\)
Vì 128 > 49 nên \(128^{10}>49^{10}\)
Vậy \(2^{70}>7^{20}\) .
\(2^{70}=14^{10}\)
\(7^{20}=7^{10}.7^{10}\)
\(\Rightarrow2^{70}>7^{20}\)