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Câu a là thế này nha \(\frac{-36}{9}\) \(\le\) x \(\le\) \(\frac{-15}{5}\)
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ở câu 1 ở mỗi phẫn số chúng ta cộng thêm 1, tổng là ta cộng thêm 5. Lấy 5 + -5=0. Rồi ta được tất cả tử là x+200,đặt chung ra ngoài,từ đó tính x=-200
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Theo đầu bài ta có:
\(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}\)
\(\Rightarrow\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}\)
\(\Rightarrow\left(\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+...+\frac{1}{x\left(x+1\right)}\right)\cdot2=\frac{2}{9}\)
\(\Rightarrow\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{1}{9}\)
\(\Rightarrow\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{18}\)
\(\Rightarrow x+1=18\)
\(\Rightarrow x=17\)
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a) \(\left(\dfrac{1}{3}-\dfrac{1}{2}\right)^{x-1}=\dfrac{1}{36}\) \(\Leftrightarrow\left(\dfrac{-1}{6}\right)^{x-1}=\dfrac{1}{36}\)
\(\Leftrightarrow\left(\dfrac{-1}{6}\right)^{x-1}=\left(\dfrac{1}{6}\right)^2\)
\(\Leftrightarrow x-1=2\Rightarrow x=3\)
b) \(\dfrac{25}{5^x}=\dfrac{1}{125}\Leftrightarrow\dfrac{25}{5^x}=\dfrac{25}{3125}\Leftrightarrow\dfrac{25}{5^x}=\dfrac{25}{5^5}\Rightarrow x=5\)
a) \(\left(\dfrac{1}{3}-\dfrac{1}{2}\right)^{x-1}=\dfrac{1}{36}\Leftrightarrow\left(-\dfrac{1}{6}\right)^{x-1}=\left(-\dfrac{1}{6}\right)^2\)
\(\Leftrightarrow x-1=2\Rightarrow x=2+1=3\)
b) \(\dfrac{25}{5^x}=\dfrac{1}{125}\Leftrightarrow\dfrac{25}{5^x}=\dfrac{25}{3125}\Leftrightarrow\dfrac{25}{5^x}=\dfrac{25}{5^5}\Rightarrow x=5\)
Giờ mới đúng thật nè
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a; => \(3^x+3^x.3+3^x.3^2=1053\)
=> \(3^x.\left(1+3+3^2\right)=1053\)
=> \(3^x.13=1053\)
=> \(3^x=81\)
=> \(3^x=3^4\)
=> x=4
b; => (x-1)^2.(x-1)=(x-1)^2
=> (x-1)^2.(x-1)-(x-1)^2=0
=> (x-1)^2.[(x-1)^2-1)=0
\(\hept{\begin{cases}x-1=0\\x-1=1\\x-1=-1\end{cases}}\)
=> \(\hept{\begin{cases}x=1\\x=2\\x=0\end{cases}}\)
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1 a, Ta có: \(36^5\): \(18^5\)= \(\left(36:18\right)^5\)= \(2^5\)= \(32\)
\(1b.\)\(24\)\(5^3\)+ \(5^2\). \(5^3\)= \(5^2\). \(\left(5^3+24\right)\)= \(25.149\)= \(3725\)
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3x+2=369
=>x+2=69
x=69-2
x=67
2x-5=810
2x-5=230
=>x-5=30
x=30+5
x=35
3x+2+3x=810
3x.32+3x=810
3x.(32+1)=810
3x.10=810
3x=810:10
3x=81
3x=34
=>x=4
5x+1-5x=500
5x.5-5x=500
5x.(5-1)=500
5x.4=500
5x=500:4
5x=125
5x=53
=>x=3
a) 3x+2 = 369
x + 2 = 69
x = 69 - 2
x = 67
b) 2x-5 = 810
2x-5 = 230
x - 5 = 30
x = 30 + 5
x = 35
c) 3x+2 + 3x = 810
3x . 9 + 3x . 1 = 810
3x . ( 9 + 1 ) = 810
3x . 10 = 810
3x = 810 : 10
3x = 81
3x = 34
=> x = 4
d) 5x+1 - 5x = 500
5x . 5 - 5x . 1 = 500
5x . ( 5 - 1 ) = 500
5x . 4 = 500
5x = 500 : 4
5x = 125
5x = 53
=> x = 3
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a) ta cs: 3645 - 3644 = 3644.(36-1) =3644.35
3644 - 3643 = 3643.35
=> 3645 - 3644 > 3644 - 3643
b) ta cs: 3450 = (33)150 = 27150
5300 = (52)150 = 25150
=> 3450 > 5300
c) ta cs: 3452 = 345.345 = 345.(342+ 3) = 345.342 + 345.3
342 . 348 = 342.(345+3) = 342.345 + 342.3
=> 3452 > 342.348
d) ta cs: (1+2+3+4)2 = 102 =100
13 + 23 + 33 + 43 = 100
=>...
3x+3x+1=36
3x(1+3)=36
3x.4=36
3x=36:4
3x=9
3x=32
x=2
Vậy x=2
3x + 3x + 1 = 36
3x . 1 + 3x . 3 = 36
3x . ( 1 + 3 ) = 36
3x . 4 = 36
3x = 36 : 4
3x = 9
3x = 32
=> x = 2.