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a/ ta co \(50^{20}=\left(50^2\right)^{10}\)
\(\left(50^2\right)^{10}=2500^{10}< 2550^{10}\)
Hay \(50^{20}< 2550^{10}\)
b/ ta có \(3^{75}=\left(3^3\right)^{25}\)
\(5^{50}=\left(5^2\right)^{25}\)
\(\Rightarrow\left(3^3\right)^{25}=27^{25}\)
\(\Rightarrow\left(5^2\right)^{25}=25^{25}\)
Vay \(3^{75}>5^{50}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{3x-40}{50}+\dfrac{3x-10+2x+60+4x-360}{40}=0\)
=> \(\dfrac{3x-40}{50}+\dfrac{9x-310}{40}=0\)
=> \(\dfrac{3x-40}{50}=\dfrac{-9x+310}{40}\)
=> \(40\left(3x-40\right)=50\left(-9x+310\right)\)
=> \(120x-1600=-450x+15500\)
=> \(120x+450x=15500+1600\)
Hay \(570x=17100\)
=>x = 30
Hơi dài nhé bạn
\(\dfrac{3x-40}{50}\)+\(\dfrac{3x-10+2x+60+4x-360}{40}\)=0
⇒\(\dfrac{3x-40}{50}\)+\(\dfrac{9x-310}{40}\)=0
⇒\(\dfrac{3x-40}{50}\)=\(\dfrac{9x-310}{40}\)
⇒40(3x -40) = 50(-9x+310)
⇒120x - 1600 = -450x + 15500
⇒120x + 450x = 15500 + 1600
Mặt khác: 570x = 17100
⇒x = 30
![](https://rs.olm.vn/images/avt/0.png?1311)
a. Ta có: \(50^{20}=50^{2.10}=2500^{10}< 2550^{10}\)
Vậy \(5^{20}< 2550^{10}\)
Ý b làm tương tự, tách 10 thành 5.2 là được.
a) 5020 và 255010
ta có : 5020=(502)10=250010
=> 250010<255010
vì 2500<2550 và 10=10
hay 5020<255010
Vậy 5020<255010
b)99910 và 9999995
Ta có : 99910 = (9992)5
9999995 = (999.1001)5
Ta thấy : (9992)=999.999
999.999 < 999.1001 vì 999<1001
=> 9992<999.1001
=>(9992)5<(999.1001)5
hay 99910<9999995
Vậy 99910< 9999995
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\left|x-30\right|-15=0\)
\(\Rightarrow\left|x-30\right|=15\)
\(\Rightarrow\left[\begin{array}{nghiempt}x-30=15\\x-30=-15\end{array}\right.\) \(\Rightarrow\left[\begin{array}{nghiempt}x=45\\x=15\end{array}\right.\)
\(a.\)
\(\left|x-30\right|-15=0\)
\(\Rightarrow\left|x-30\right|=0+15=15\)
\(\Rightarrow\left[\begin{array}{nghiempt}x-30=15\\x-30=-15\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}x=15+30=45\\x=-15+30=15\end{array}\right.\)
Vậy \(\left[\begin{array}{nghiempt}x=45\\x=15\end{array}\right.\)
\(b.\)
\(\left|20-x\right|-5=10\)
\(\Rightarrow\left|20-x\right|=10+5=15\)
\(\Rightarrow\left[\begin{array}{nghiempt}20-x=15\\20-x=-15\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}x=20-15=5\\x=-20-15=-35\end{array}\right.\)
Vậy \(\left[\begin{array}{nghiempt}x=5\\x=-35\end{array}\right.\)
\(c.\)
\(\left|20-x\right|+6=0\)
\(\Rightarrow\left|20-x\right|=0-6=-6\)
\(\Rightarrow x\in\varnothing\)
\(d.\)
\(\left|x-50\right|=0\)
\(\Rightarrow x-50=0\)
\(\Rightarrow x=0+50=50\)
Vậy \(x=50\)
\(e.\)
\(\frac{\left|x-10\right|}{30}=3\)
\(\Rightarrow\left|x-10\right|=3.30=90\)
\(\Rightarrow\left[\begin{array}{nghiempt}x-10=90\\x-10=-90\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}x=90+10=100\\x=-90+10=-80\end{array}\right.\)
Vậy \(\left[\begin{array}{nghiempt}x=100\\x=-80\end{array}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Theo đề bài ta có: Trung bình cộng: 66,5
=> 40.3+50.4+60.4+x.5+90.3+100.1 / 20 = 66,5
=> 930+5x = 66,5.20
=> 930+5x = 1330
=> 5x = 1330-930
=> 5x = 400
=> x = 400/5 = 80
Chúc bạn học tốt ^^
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a) Ta có : (1/16)10 = [(1/2)4]10 = (1/2)40
Vì (1/2)40 < (1/2)50 nên (1/16)10 < (1/2)50
b) Ta có : 430 = ( 2 . 2)30 = 230 . 230 = (22)15 . (23)10 > 315 . 810 > 3 . 310 .810 = 3 . (3 . 8)10 = 3 .2410
Vậy nên 230 + 330 + 430 > 2410 . 3
Mình chỉ giải thế thôi, còn đâu bn tự làm tiếp
ta có : 1010 = (102)5= 1005 = ( 2.50) 2= 25.505
mà 25 = 38 <40
=> 1010< 40 . 505
1010=(102)5=1005=( 2.50 )5=25.505=32.505<40.505
=> 1010 < 40.505
!!!