1.Tìm x \(\in\)N, biết:
a) \(25< 3^x< 220\)
b) \(49< 7^x< 2500\)
c) \(25< 3^x< 250\)
2. Cho S= \(1+2+2^2+.....+2^9\). Thu gọn S rồi so sánh S với 5 x \(2^8\).
Giải sớm giùm mik nha!!! Thanks
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a) 5^x=5^78:5^14(lấy 78-14)
5^x=5^64
=> x=64
b) 7^x.7^2=7^21
7^x=7^21:7^2
7^x=7^19
=> x=19
1. \(A=\left(2^{2017}\cdot3+2^{2017}\cdot5\right):2^{2018}\)
\(A=\left[2^{2017}.\left(3+5\right)\right]:\left(2^{2018}\right)\)
\(A=\left[2^{2017}.2^3\right]:\left(2^{2018}\right)\)
\(A=2^{2020}:2^{2018}=2^2=4\)
2. a) 2 + x : 5 = 6
=> x : 5 = 4
=> x = 20
b) 5x(7 + 48:x) = 45
=> x(7 + 48:x) = 9
=> 7x + 48 = 9
=> 7x = -39
=> x = -39/7.
c) Không hiểu đề câu này cho lắm.
3. \(25^{30}=\left(5^2\right)^{30}=5^{60};125^{19}=\left(5^3\right)^{19}=5^{57}\)
Vì 60 > 57 => \(25^{30}>125^{19}\)
4. \(S=1+7^1+...+7^{100}\)
\(\Rightarrow7S=7+7^2+...+7^{101}\)
\(\Rightarrow7S-S=7+7^2+...+7^{101}-1-7-...-7^{100}\)
\(\Rightarrow6S=7^{101}-1\)
\(\Rightarrow S=\frac{7^{101}-1}{6}\)
5. \(Q=1+2+2^2+...+2^{49}\)
\(\Rightarrow2Q=2+2^2+...+2^{50}\)
\(\Rightarrow2Q-Q=2+2^2+...+2^{50}-1-2-...-2^{49}\)
\(\Rightarrow Q=2^{50}-1\)
\(\Rightarrow2^{50}-1+1=2^n\)
\(\Rightarrow2^{50}=2^n\Rightarrow n=50\)
a)S = 1 + 2 + 22 + 23 + 24 +25 +26 +27 + 28 + 29
2S = 2.(1 + 2 + 22 + 23 + 24 +25 +26 +27 + 28 + 29)
2S = 2 + 22 + 23 + 24 +25 +26 +27 + 28 + 29 + 210
S = (2 + 22 + 23 + 24 +25 +26 +27 + 28 + 29 + 210) - (1 + 2 + 22 + 23 + 24 +25 +26 +27 + 28 + 29)
S = 210 - 1
Suy ra: S = \(\frac{2^{9+1}-1}{2-1}\)
S = \(\frac{2^{10}-1}{1}\)
S = 210 - 1
S = 1023
b)Mình không thể giúp bạn vì mình không rõ 5.28 hay (5.2)8
1.
a, (x+50)*2=220
=> 2x+100=220
=> 2x = 120
=> x= 60
b, (2x-75)*12=144
=> 24x-900=144
=> 24x=1044
=> x= 43,5
c, (47-3x)=5
=> 47-3x=5
=> 3x=42
=> x= 14
A. ( x + 50 ) x 2= 220
=> 2x + 100 = 220
=> 2x = 220 - 100
=> 2x = 120
=> x = 120 : 2
=> x = 60
B. ( 2x - 75 ) x 12 = 144
=> (2x - 75) x 12 = 144
=> 2x - 75 = 144 : 12
=> 2x - 75 = 12
=> 2x = 75 + 12
=> 2x = 87
=> x = 87 : 2 = 43,5
C. 47 - 3x = 5
=> 3x = 47 - 5 = 42
=> x = 42 : 3
=> x = 14.
2)1 + 2 + 3 + 4 + 5 +..+ X = 2550
=> \(\frac{x.\left(x+1\right)}{2}\)=2550
=> x.(x+1) = 2550 x 2 = 5100. Mà không có 2 số liên tiếp nào nhân với nhau bằng 5100 nên x không thỏa mãn đề bài.
3)Đề sai nha bạn.
a) ĐKXĐ: \(x\ne1\)
Ta có: \(x^2-8x+7=0\)
\(\Leftrightarrow x^2-x-7x+7=0\)
\(\Leftrightarrow x\left(x-1\right)-7\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-7=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\left(loại\right)\\x=7\left(nhận\right)\end{matrix}\right.\)
Thay x=7 vào B, ta được:
\(B=\dfrac{1}{7-1}=\dfrac{1}{6}\)
Vậy: Khi \(x^2-8x+7=0\) thì \(B=\dfrac{1}{6}\)
b) Ta có: \(A=\dfrac{x^2+2}{x^3-1}+\dfrac{x+1}{x^2+x+1}\)
\(=\dfrac{x^2+2}{\left(x-1\right)\left(x^2+x+1\right)}+\dfrac{\left(x+1\right)\left(x-1\right)}{\left(x^2+x+1\right)\left(x-1\right)}\)
\(=\dfrac{x^2+2+x^2-1}{x^3-1}\)
\(=\dfrac{2x^2+1}{x^3-1}\)
a)
\(\left(x-\dfrac{2}{3}\right):\dfrac{1}{2}=\dfrac{5}{7}\)
\(\Rightarrow x-\dfrac{2}{3}=\dfrac{5}{7}\) x \(\dfrac{1}{2}\)
\(\Rightarrow x-\dfrac{2}{3}=\dfrac{5}{14}\)
\(\Rightarrow x=\dfrac{5}{14}+\dfrac{2}{3}\)
\(\Rightarrow x=\dfrac{15}{42}+\dfrac{2}{42}\)
\(\Rightarrow x=\dfrac{17}{42}\)
b)
\(x\) x \(\dfrac{1}{2}=1-\dfrac{1}{3}\)
\(x\) x \(\dfrac{1}{2}=\dfrac{3}{3}-\dfrac{1}{3}\)
\(x\) x \(\dfrac{1}{2}=\dfrac{2}{3}\)
\(\Rightarrow x=\dfrac{2}{3}:\dfrac{1}{2}\)
\(\Rightarrow x=\dfrac{2}{3}\) x \(2=\dfrac{4}{3}\)
c)
\(\dfrac{26}{5}-x=\dfrac{9}{15}\) x \(\dfrac{25}{3}\)
\(\dfrac{26}{5}-x=5\)
\(\Rightarrow x=\dfrac{26}{5}-5\)
\(\Rightarrow x=\dfrac{26}{5}-\dfrac{25}{5}\)
\(\Rightarrow x=\dfrac{1}{5}\)
1,2 dễ ko làm
3,
S = 1 + 2 + 22 + 23 + ... + 29
2S = 2 + 22 + 23 + 24 + ... + 210
2S - S = ( 2 + 22 + 23 + 24 + ... + 210 ) - ( 1 + 2 + 22 + 23 + ... + 29 )
S = 210 - 1
Mà 5 . 28 = ( 1 + 22 ) . 28 = 28 + 210 > 210 > 210 - 1
Vậy S < 5 . 28
P = 1 + 3 + 32 + 33 + ... + 320
3P = 3 + 32 + 33 + 34 + ... + 321
3P - P = ( 3 + 32 + 33 + 34 + ... + 321 ) - ( 1 + 3 + 32 + 33 + ... + 320 )
2P = 321 - 1
P = ( 321 - 1 ) : 2 < 321
Vậy P < 321
a,S=1+3+32+...+360
3S=3+32+33+...+361
3S-S=(3+32+33+...+361)-(1+3+32+...+360)
2S = 361 - 1
b,2S+1=361-1+1=361 = 3x-3
=>x-3=61=>x=64
c, S=1+3+32+...+360
=(1+3)+(32+33)+...+(359+360)
=4+32(1+3)+...+359(1+3)
=4+32.4+...+359.4
=4(1+32+...+359) chia hết cho 4
S=1+3+32+...+360
=(1+3+32)+....+(358+359+360)
=13+...+358(1+3+32)
=13+...+358.13
=13(1+...+358)
\(S=1+2+2^2+.....+2^9\)
\(2S=2\left(1+2+2^2+2^3+.....+2^9\right)\)
\(2S=2+2^2+2^3+2^4+....+2^{10}\)
\(2S-S=\left(2+2^2+2^3+2^4+....+2^{10}\right)-\left(1+2+2^2+....+2^9\right)\)
\(S=2^{10}-1\)
Gọi: \(X=5.2^8\)
\(X=\left(1+4\right).2^8\)
\(X=1.2^8+4.2^8\)
\(X=2^8+2^2.2^8\)
\(X=2^8+2^{10}\)
\(S< X\)