( 1/3 ) ^x + ( 1 / 3 ) ^{x - 2} = 10 / 243

( 1 / 3 ) ^x ( 1 + ( 1/3 ) ^-2  = 10 / 243

( 1 / 3 ) ^x . 10                = 10 / 243

( 1 / 3 ) ^x                       = 1/243

( 1 / 3 ) ^x                       = ( 1/3 ) ⁵

=> x = 5

5.trong violympic đúng ko bạn

hùng sai chắc luôn vừa cô giáo bảo xong

1: =>3^x=81

=>x=4

2: =>2^x=8

=>x=3

3: =>x^3=2^3

=>x=2

4: =>x^20-x=0

=>x(x^19-1)=0

=>x=0 hoặc x=1

5: =>2^x=32

=>x=5

6: =>(2x+1)^3=9^3

=>2x+1=9

=>2x=8

=>x=4

7: =>x^3=115

=>\(x=\sqrt[3]{115}\)

8: =>(2x-15)^5-(2x-15)^3=0

=>(2x-15)^3*[(2x-15)^2-1]=0

=>2x-15=0 hoặc (2x-15)^2-1=0

=>2x-15=0 hoặc 2x-15=1 hoặc 2x-15=-1

=>x=15/2 hoặc x=8 hoặc x=7

1. Tìm số tự nhiên x biết:

1) \(3^x.3=243\)

\(3^x=243:3\)

\(3^x=81\)

\(3^x=3^4\)

\(\Rightarrow x=4\)

_____

2) \(7.2^x=56\)

\(2^x=56:7\)

\(2^x=8\)

\(2^x=2^3\)

\(\Rightarrow x=3\)

_____

3) \(x^3=8\)

\(x^3=2^3\)

\(\Rightarrow x=3\)

_____

4) \(x^{20}=x\)

\(x^{20}-x=0\)

\(x\left(x^{19}-1\right)=0\)

\(\Rightarrow x=0\) hoặc \(x=1\)

5) \(2^x-15=17\)

\(2^x=17+15\)

\(2^x=32\)

\(2^x=2^5\)

\(\Rightarrow x=5\)

_____

6) \(\left(2x+1\right)^3=9.81\)

\(\left(2x+1\right)^3=729=9^3\)

\(\rightarrow2x+1=9\)

\(2x=9-1\)

\(2x=8\)

\(x=8:2\)

\(\Rightarrow x=4\)

_____

7) \(x^6:x^3=125\)

\(x^3=125\)

\(x^3=5^3\)

\(\Rightarrow x=5\)

_____

8) \(\left(2x-15\right)^5=\left(2x-15\right)^3\)

\(\rightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\)

\(\left(2x-15\right)^3.\left[\left(2x-15\right)^2-1\right]=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\x=7\\x=8\end{matrix}\right.\)

_____

9) \(3^{x+2}-5.3^x=36\)

\(3^x.\left(3^2-5\right)=36\)

\(3^x.\left(9-5\right)=36\)

\(3^x.4=36\)

\(3^x=36:4\)

\(3^x=9\)

\(3^x=3^2\)

\(\Rightarrow x=2\)

_____

10) \(7.4^{x-1}+4^{x+1}=23\)

\(\rightarrow7.4^{x-1}+4^{x-1}.4^2=23\)

\(4^{x-1}.\left(7+4^2\right)=23\)

\(4^{x-1}.\left(7+16\right)=23\)

\(4^{x-1}.23=23\)

\(4^{x-1}=23:23\)

\(4^{x-1}=1\)

\(4^{x-1}=4^1\)

\(\rightarrow x-1=0\)

\(x=0+1\)

\(\Rightarrow x=1\)

Chúc bạn học tốt

\(\left(x-3\right)^5=243=3^5\Rightarrow x-3=3\Leftrightarrow x=3+3=6\)

\(x\left(x+y\right)=2\Rightarrow xx+xy=2\Rightarrow x=1;y=1\left(TM\right)\)

\(\left(x+2\right)^5=2^{10}=4^5\Rightarrow x+2=4\Leftrightarrow x=4-2=2\)

\(1+2+3+...+x=78\Rightarrow\frac{x\left(x+1\right)}{2}=78\)

\(\Rightarrow x\left(x+1\right)=78\times2=156=12\times13\Rightarrow x=12\)

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mk play nè

\(\left(\dfrac{1}{3}\right)^x+\left(\dfrac{1}{3}\right)^{x+2}=\dfrac{10}{243}\)

\(\left(\dfrac{1}{3}\right)^x+\left(\dfrac{1}{3}\right)^x.\left(\dfrac{1}{3}\right)^2=\dfrac{10}{243}\)

\(\left(\dfrac{1}{3}\right)^x.\left[1+\left(\dfrac{1}{3}\right)^2\right]=\dfrac{10}{243}\)

\(\left(\dfrac{1}{3}\right)^x.\dfrac{10}{9}=\dfrac{10}{243}\)

\(\left(\dfrac{1}{3}\right)^x=\dfrac{10}{243}:\dfrac{10}{9}\)

\(\left(\dfrac{1}{3}\right)^x=\dfrac{1}{27}\)

\(\left(\dfrac{1}{3}\right)^x=\left(\dfrac{1}{3}\right)^3\)

\(\Rightarrow x=3\)

\(\left(x-1,2\right)^2=4\)

⇔\(x^2-2.x.1,2+1,2^2=4\)

⇔\(x^2-2,4x+1,44=4\)

⇔\(x^2-2,4x=4-1,44\)

⇔\(x\left(x-2,4\right)=2,56\)

⇔\(x=2,56\) hoặc \(x-2,4=2,56\)

⇔\(x=2,56\) hoặc \(x=4,96\)

a) \(\left(x-1,2\right)^2=4=2^2\)

\(\Leftrightarrow x-1,2=4\)

\(\Leftrightarrow x=5,2\)

b) \(\left(x+1\right)^3=-125=\left(-5\right)^3\)

\(\Leftrightarrow x+1=-5\)

\(\Leftrightarrow x=-6\)

c) \(\left(x+1,5\right)^8+\left(2,7-y\right)^{10}=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}x+1,5=0\\2,7-y=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=-1,5\\y=2,7\end{matrix}\right.\)

a) \(3^{2x-1}=243\)

\(\Leftrightarrow3^{2x-1}=3^5\)

\(\Leftrightarrow2x-1=5\)

\(\Leftrightarrow2x=5+1\)

\(\Leftrightarrow2x=6\)

\(\Leftrightarrow x=\dfrac{6}{2}\)

\(\Leftrightarrow x=3\)

Vậy \(x=3\)

b) \(\left(3^x\right)^2:3^3=\dfrac{1}{243}\)

\(\Leftrightarrow3^{2x}:3^3=\dfrac{1}{3^5}\)

\(\Leftrightarrow3^{2x}:3^3=3^{-5}\)

\(\Leftrightarrow3^{2x-3}=3^{-5}\)

\(\Leftrightarrow2x-3=-5\)

\(\Leftrightarrow2x=-5+3\)

\(\Leftrightarrow2x=-2\)

\(\Leftrightarrow x=-\dfrac{2}{2}\)

\(\Leftrightarrow x=1\)

Vậy \(x=1\)

c) \(2^{3x+2}=4^{x+5}\)

\(\Leftrightarrow2^{3x+2}=\left(2^2\right)^{x+5}\)

\(\Leftrightarrow2^{3x+2}=2^{2\left(x+5\right)}\)

\(\Leftrightarrow3x+2=2\left(x+5\right)\)

\(\Leftrightarrow3x+2=2x+10\)

\(\Leftrightarrow3x-2x=10-2\)

\(\Leftrightarrow x=8\)

Vậy \(x=8\)

d) \(3^{x+1}=9^x\)

\(\Leftrightarrow3^{x+1}=\left(3^2\right)^x\)

\(\Leftrightarrow3^{x+1}=3^{2x}\)

\(\Leftrightarrow x+1=2x\)

\(\Leftrightarrow2x-x=1\)

\(\Leftrightarrow x=1\)

Vậy \(x=1\)

3^x + 3^x+1 + 3^x+2 = 243

3^x . 1 +3^x . 3¹ + 3^x .3² = 243

3^x .(1 + 3 + 3²) = 243

3^x .(1 +3 + 9) = 243

3^x . 13 = 243

3^x = 243 : 13

Vì 243 : 13 không thuộc N => x thuộc rỗng

 x²³:216=x¹⁵.x⁵

x²³: 6³= x²⁰

==> 6³=x²³:x²⁰

==> 6³=x³

==> x=6

(5^x.5^x+2):5³=125

==> 5^2x+2:5³=5³

==> 5^2x+2=5³.5³

==> 5^2x+2=5⁶

==> 2x+2=6

2x=6–2

2x=4

x=4:2

x=2

(3^x.3^x+4):3³=243

==> 3^2x+4:3³=3⁵

3^2x+4=3⁵.3³

3^2x+4=3⁸

==> 2x+4=8

2x=8–4

2x=4

x=4:2

x=2

3^x+3^x+1+3^x+2=243

3^x.1+3^x.3¹+3^x.3²=243

3^x.(1+3¹+3²)=243

3^x. (1+3+9)=243

3^x.13=243

3^x=243:13

3^x=...

`#3107.101107`

a)

\(27< 3^x< 243\\ \Rightarrow3^3< 3^x< 3^5\\ \Rightarrow3< x< 5\\ \Rightarrow x=4\)

Vậy, `x = 4`

b)

\(2^x+2^{x+1}+2^{x+2}=56?\\ \Rightarrow2^x+2^x\cdot2+2^x\cdot4=56\\ \Rightarrow2^x\cdot\left(1+2+4\right)=56\\ \Rightarrow2^x\cdot7=56\\ \Rightarrow2^x=8\\ \Rightarrow2^x=2^3\\ \Rightarrow x=3\)

Vậy, `x = 3`

c)

\(3^x+3^{x+2}=810\\ \Rightarrow3^x+3^x\cdot9=810\\ \Rightarrow3^x\cdot\left(1+9\right)=810\\ \Rightarrow3^x\cdot10=810\\ \Rightarrow3^x=81\\ \Rightarrow3^x=3^4\\ \Rightarrow x=4\)

Vậy, `x = 4.`

a) \(27< 3^x< 243\)

\(\Rightarrow3^3< 3^x< 3^5\)

\(\Rightarrow3< x< 5\)

c) \(3^x+3^{x+2}=810\)

\(\Rightarrow3^x\left(1+3^2\right)=810\)

\(\Rightarrow3^x.10=810\)

\(\Rightarrow3^x=810:10\)

\(\Rightarrow3^x=81\)

\(\Rightarrow3^x=3^4\)

\(\Rightarrow x=4\)