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Ta có :
\(A=3+3^2+3^3+3^4+3^5+3^6+...+3^{58}+3^{59}+3^{60}\)
\(\Rightarrow A=\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+...+\left(3^{58}+3^{59}+3^{60}\right)\)
\(\Rightarrow A=3.\left(3^0+3^1+3^2\right)+3^4.\left(3^0+3^1+3^2\right)+...+3^{58}.\left(3^0+3^1+3^2\right)\)
\(\Rightarrow A=3.13+3^4.13+3^7.13+..+3^{58}.13\)
\(\Rightarrow A=\left(3+3^4+...+3^{58}\right).13⋮13\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(3^x+4\cdot3^{x-2}=333\)
\(\Rightarrow3^{x-2+2}+4\cdot3^{x-2}=333\)
\(\Rightarrow3^{x-2}\cdot\left(3^2+4\right)=333\)
\(\Rightarrow3^{x+2}\cdot\left(9+4\right)=333\)
\(\Rightarrow3^{x+2}\cdot13=333\)
\(\Rightarrow3^{x+2}=333:13\)
\(\Rightarrow3^{x+2}=\dfrac{333}{13}\)
Không có x nào thỏa mãn
⇒ x ∈ ∅
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a. ( 2x + 1 )2 = 49
<=> ( 2x + 1 )2 = 72
<=> 2x + 1 = 7
<=> x = 3
b. ( 2x - 1 )4 = 81
<=> ( 2x - 1 )4 = 34
<=> 2x - 1 = 3
<=> x = 2
c. ( x + 1 )3 = 2x3
<=> x + 1 = 2x
<=> x = 1
d. ( 2x + 1 )3 = 3x3
<=> 2x + 1 = 3x
<=> x = 1
( 2x + 1 )2 = 49
<=> ( 2x + 1 )2 = ( ±7 )2
<=> \(\orbr{\begin{cases}2x+1=7\\2x+1=-7\end{cases}}\Rightarrow\orbr{\begin{cases}x=3\\x=-4\end{cases}}\)
( 2x - 1 )4 = 81
<=> ( 2x - 1 )4 = ( ±3 )4
<=> \(\orbr{\begin{cases}2x-1=3\\2x-1=-3\end{cases}}\Rightarrow\orbr{\begin{cases}x=2\\x=-1\end{cases}}\)
( x + 1 )3 = ( 2x )3
<=> x + 1 = 2x
<=> x - 2x = -1
<=> -x = -1
<=> x = 1
( 2x + 1 )3 = ( 3x )3
<=> 2x + 1 = 3x
<=> 2x - 3x = -1
<=> -x = -1
<=> x = 1
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1)5x+1 + 6.5x+1 = 875
5x+1 ( 1+6 ) = 875
5x+1 . 7 = 875
5x+1 = 875 : 7
5x+1 = 125
5x+1 = 53
x+1 = 3
x = 3 - 1
x = 2
2)3x+1 + 3x+3 = 810
3x . 3 + 32 . 3x+1 = 810
3x . 3 + 9 . 3x . 3 = 810
3x .3 ( 1 + 9 ) = 810
3x+1 . 10 = 810
3x+1 = 810 : 10
3x+1 = 81
3x+1 = 34
x+1 = 4
x = 4-1
x = 3
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a) \(3\left(2x-5\right)+125=134\)
\(\Leftrightarrow3\left(2x-5\right)=9\)
\(\Leftrightarrow2x-5=3\)
\(\Leftrightarrow2x=8\Leftrightarrow x=4\)
b) \(\left(2x+5\right)+\left(2x+3\right)+\left(2x+1\right)=27\)
\(\Leftrightarrow6x+9=27\)
\(\Leftrightarrow6x=18\Leftrightarrow x=3\)
d) \(27\left(x-27\right)-27=0\)
\(\Leftrightarrow27\left(x-27\right)=27\)
\(\Leftrightarrow x-27=1\Leftrightarrow x=28\)
\(2x+14=\left(-1\right)^{99}+x\)
\(2x-x=-1-14\)
\(\Rightarrow x=-15\)
Vậy x = -15