So sanh:
a/ \(2^{225}\) va \(3^{150}\)
b/ \(3^{34}\) va \(5^{21}\)
c/ \(3^{21}\) va \(2^{31}\)
d/ \(2^{91}\) va \(5^{35}\)
e/ \(99^{20}\) va \(9999^{10}\)
f/ \(12^8.9^{12}\) va \(18^{16}\)
g/ \(75^{20}\) va \(45^{10}.5^{30}\)
a, 2225 = 215.15= ( 215)15 = 3276815
3150 = 310.15 = ( 310)15 = 5904915
Dễ thấy 32768 < 59049 nên 2225 < 3150
hay so sanh:
99^20 va 9999^10
54^4 va 21^12
71^5 va 17^20
2^30+3^20+4^30 va 3x 24^10
\(99^{20}< 9999^{10}\)
\(54^4< 21^{12}\)
\(71^5< 17^{20}\)
\(2^{30}+3^{20}+4^{30}>3\times24^{10}\)
SO sanh cac so sau
a,107^50va 73^75
b,54^4va 21^12
c,2^91 va 5^35
d,3^500 va 7^300
e, 122^26 va 10^51
g,124^30 va 625^23
a. \(107^{50}< 73^{75}\)
b. \(54^4< 21^{12}\)
c. \(2^{91}>5^{35}\)
d. \(3^{500}>7^{300}\)
e. \(122^{26}< 10^{51}\)
g. \(124^{30}>625^{23}\)
so sanh
224va 316
9920va 999910
291va 535
2^24 = (2^3)^8 = 8^8
3^16 = (3^2)^8 = 9^8
Vì 8^8 < 9^8 => 2^24 < 3^16
99^20 = 99^10 . 99^10 < 99^10 . 101^110 = (99.101)^10 = 9999^10
=> 99^20 < 9999^10
2^91 = (2^13)^7 = 8192^7
5^35 = (5^5)^7 = 3125^7
Vì 8192^7 > 3125^7 => 2^91 > 5^35
k mk nha
so sanh 2 mu 36 va 3 mu 27
9 mu 20 va 9999 mu 10
54 mu 4 va 21 mu 12
viet cach lam luon nha
Ta có:\(2^{36}\)và \(3^{27}\)
\(2^{36}=\left(2^4\right)^9=16^9\)
\(3^{27}=\left(3^3\right)^9=27^9\)
Vì \(16< 27\Rightarrow16^9< 27^9\)
Vậy....
b,\(9^{20}\)và \(9999^{10}\)
\(9^{20}=\left(9^2\right)^{10}=81^{10}\)
\(9999^{10}\)
Vì \(81< 9999\Rightarrow81^{10}< 9999^{10}\)
Vậy ...
c,\(54^4\)
\(21^{12}=\left(21^3\right)^4=9261^4\)
Vì \(54< 9261\Rightarrow54^4< 9261^4\)
Vậy...
1so sanh cac phan so sau
a,2/3 va -1/4
b -7/10 va 7/-8
c 6/7 va 3/5
d -14/21 va 60/-72
e 16/9 va24/13
g 27/82 va 26/75
1)tim x bit a)(1/2-1/3).6^x+6^x+2=6^15+6^18
b)3^x+3^x+2=2430
c)(2x-15)^5=(2x-15)^3
2) so saanh
a)2^11 va 5^35
b)2^31 va 3^21
c)2^15 va 27^5.49^8 d)21^15 va 27^5.49^8
1)tim x bit a)(1/2-1/3).6^x+6^x+2=6^15+6^18
b)3^x+3^x+2=2430
c)(2x-15)^5=(2x-15)^3
2) so saanh a)2^11 va 5^35
b)2^31 va 3^21
c)2^15 va 27^5.49^8 d)21^15 va 27^5.49^8
1.
b) \(3^x+3^{x+2}=2430\)
\(\Rightarrow3^x.1+3^x.3^2=2430\)
\(\Rightarrow3^x.\left(1+3^2\right)=2430\)
\(\Rightarrow3^x.10=2430\)
\(\Rightarrow3^x=2430:10\)
\(\Rightarrow3^x=243\)
\(\Rightarrow3^x=3^5\)
\(\Rightarrow x=5\)
Vậy \(x=5.\)
c) \(\left(2x-15\right)^5=\left(2x-15\right)^3\)
\(\Rightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\)
\(\Rightarrow\left(2x-15\right)^3.\left[\left(2x-15\right)^2-1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x-15=0\\\left(2x-15\right)^2=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=15\\2x-15=\pm1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=15:2\\2x-15=1\\2x-15=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{15}{2}\\2x=16\\2x=14\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{15}{2}\\x=8\\x=7\end{matrix}\right.\)
Vậy \(x\in\left\{\frac{15}{2};8;7\right\}.\)
Chúc bạn học tốt!
so sanh 21^15 va 27^5
15^12 va 81^3.125^5
3^39 va 11^21
72^45-72^44 va 72^44-72^43
199^20 va 2003^15
a) \(21^{15}=21^{3.5}=\left(21^3\right)^5=9261^5\)
Vì \(9261>27\Rightarrow9261^5>27^5\Rightarrow21^{15}>27^5\)
b) \(15^{12}=\left(3.5\right)^{12}=3^{12}.5^{12}\)
\(81^3.125^5=\left(3^4\right)^3.\left(5^3\right)^5=3^{4.3}.5^{3.5}=3^{12}.5^{15}\)
Vì \(3^{12}=3^{12}\)mà \(5^{12}< 5^{15}\Rightarrow3^{12}.5^{12}< 3^{12}.5^{15}\Rightarrow15^{12}< 81^3.125^5\)
