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a)\(1024^9=\left(2^{10}\right)^9=2^{90}< 2^{100}\)
b)\(27^{11}=\left(3^3\right)^{11}=3^{33}>3^{32}=\left(3^4\right)^8=81^8\)
c)\(5^{20}=\left(5^2\right)^{10}=25^{10}\)
\(3^{30}=\left(3^3\right)^{10}=27^{10}\)
Ta có: \(25^{10}< 27^{10}\)
\(\Rightarrow5^{20}< 3^{30}\)
d) tương tự
e) \(78^{12}-78^{11}=78^{11}.\left(78-1\right)=78^{11}.77\)
\(78^{11}-78^{10}=78^{10}.\left(78-1\right)=78^{10}.77\)
Ta có: \(78^{11}.77>78^{10}.77\)
\(\Rightarrow78^{12}-78^{11}>78^{11}-78^{10}\)
f) \(333^{444}=\left[\left(111.3\right)^4\right]^{111}=\left(111^4.3^4\right)^{111}=\left(111^4.81\right)^{111}\)
\(444^{333}=\left[\left(111.4\right)^3\right]^{111}=\left(111^3.4^3\right)^{111}=\left(111^3.64\right)^{111}\)
Ta có: \(111^4.81>111^3.64\)
\(\Rightarrow\left(111^4.81\right)^{111}>\left(111^3.64\right)^{111}\)
\(\Rightarrow333^{444}>444^{333}\)
Tham khảo nhé~
a) Ta có :
\(1024^9=\left(2^{10}\right)^9=2^{90}\)
Vì \(2^{100}>2^{90}\)\(\Rightarrow\)\(2^{100}>1024^9\)
Vậy \(2^{100}>1024^9\)
b) Ta có :
\(27^{11}=\left(3^3\right)^{11}=3^{33}\)
\(81^8=\left(3^4\right)^8=3^{32}\)
Vì \(3^{33}>3^{32}\)\(\Rightarrow\)\(27^{11}>81^8\)
Vậy \(27^{11}>81^8\)
c) Ta có :
\(5^{20}=\left(5^2\right)^{10}=25^{10}\)
\(3^{30}=\left(3^3\right)^{10}=27^{10}\)
Vì \(25^{10}< 27^{10}\)\(\Rightarrow\)\(5^{20}< 3^{30}\)
Vậy \(5^{20}< 3^{30}\)
d) Ta có :
\(2^{300}=\left(2^3\right)^{100}=8^{100}\)
\(3^{200}=\left(3^2\right)^{100}=9^{100}\)
Vì \(8^{100}< 9^{100}\)\(\Rightarrow\)\(2^{300}< 3^{200}\)
Vậy \(2^{300}< 3^{200}\)
e) Ta có :
\(78^{12}-78^{11}=78^{11}.\left(78-1\right)=78^{11}.77\)
\(78^{11}-78^{10}=78^{10}\left(78-1\right)=78^{10}.77\)
Vì \(78^{11}>78^{10}\)\(\Rightarrow78^{11}.77>78^{10}.77\)
Hay \(78^{12}-78^{11}>78^{11}-78^{10}\)
Vậy \(78^{12}-78^{11}>78^{11}-78^{10}\)
f) Ta có :
\(333^{444}=\left(333^4\right)^{111}=\left[\left(3.111\right)^4\right]^{111}=\left(3^4.111^4\right)^{111}=\left(81.111^4\right)^{111}\)
\(444^{333}=\left(444^3\right)^{111}=\left[\left(4.111\right)^3\right]^{111}=\left(4^3.111^3\right)^{111}=\left(64.111^3\right)^{111}\)
Vì \(81.111^4>64.111^3\)\(\Rightarrow\)\(\left(81.111^4\right)^{111}>\left(64.111^3\right)^{111}\)
Hay \(333^{444}>444^{333}\)
Vậy \(333^{444}>444^{333}\)
_Chúc bạn học tốt_
Bài 1:
\(a,8.6+288.\left(x+3\right)^2=50\\ \Leftrightarrow48+288\left(x+3\right)^2=50\\ \Leftrightarrow\left(x+3\right)^2=\dfrac{1}{144}\\ \Leftrightarrow x+3\in\left\{-\dfrac{1}{12};\dfrac{1}{12}\right\}\\ \Leftrightarrow x\in\left\{-\dfrac{37}{12};-\dfrac{35}{12}\right\}\\ Vậy.....\)
\(b,\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=5750\)
=>Số lượng số hạng của tổng trên là (x+100-x-1):1+1=100(số hạng)
\(\Rightarrow\dfrac{\left(2x+101\right).100}{2}=5750\\ \Rightarrow2x+101=\dfrac{5750.2}{100}\\ \Rightarrow2x+101=115\\ \Rightarrow2x=14\\ \Rightarrow x=7\\ Vậy........\)
\(a)16^{19}=\left(8\times2\right)^{19}=8^{19}\times2^{19}>8^{19}>8^{15}\)
\(\Rightarrow16^{19}>8^{15}\)
\(b)81^8=\left(3^4\right)^8=3^{24}< 3^{33}=\left(3^3\right)^{11}=27^{11}\)
\(\Rightarrow27^{11}>81^8\)
\(c)625^5=\left(5^4\right)^5=5^{20}< 5^{21}=\left(5^3\right)^7=125^7\)
\(\Rightarrow125^7>625^5\)
\(d)244^{11}>243^{11}=\left(3^5\right)^{11}=3^{55}>3^{52}=\left(3^4\right)^{13}=81^{13}>80^{13}\)
\(\Rightarrow244^{11}>80^{13}\)
\(d)31^{17}>17^{17}>17^{14}\)
\(\Rightarrow31^{17}>17^{14}\)
a , >
b , ?????
c , >
Câu b là dấu < , bạn ak ^^!