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

\(\dfrac{5}{8}x-\dfrac{1}{3}x-\dfrac{1}{6}x=15\)

\(\Rightarrow x\left(\dfrac{5}{8}-\dfrac{1}{3}-\dfrac{1}{6}\right)=15\)

\(\Rightarrow x\left(\dfrac{15}{24}-\dfrac{8}{24}-\dfrac{4}{24}\right)=15\)

\(\Rightarrow x.\dfrac{3}{24}=15\)

\(\Rightarrow x.\dfrac{1}{8}=15\Rightarrow x=15:\dfrac{1}{8}=15.\dfrac{8}{1}=120\)

6/5  dm³  =  1200 cm³

35 lít  =  35000 cm³

5,4 giờ  =  5 giờ  24 phút

    \(82,5-x=30,2\times2,1\)

\(\Leftrightarrow\)\(82,5-x=63,42\)

\(\Leftrightarrow\)\(x=82,5-62,42=19,08\)

Vậy....

1) 

a) 63 : 3² + 7 . 2³

= 63 : 9 + 7 . 4 

= 7 + 7 . 4 

= 7 + 28 

= 35

b) 2³ . 15 - [ 115 - 15 . ( 13 - 11 )² ] 

= 8 . 15 - [ 115 - 15 . 2² ] 

= 8 . 15 - [ 115 - 15 . 4 ] 

= 8 . 15 - [ 115 - 60 ] 

= 8 . 15 - 55

= 120 - 55 

= 65 

c) 53 . 46 + 54 . 74 - 54 . 21 

= 53 . 46 + 54 . ( 74 - 21 ) 

= 53 . 46 + 54 . 53 

= 53 . ( 46 + 54 ) 

= 53 . 100

= 5300

2) 

a) 3x - 5 = 2 

3x = 2 + 5 

3x = 7 

x = 7 : 3 

x = 2,33333....33 ( có 11 chữ số 3 nhưng 2,3333...33 không phải là số tự nhiên ) 

b) 46 + 6 ( x - 5 ) = 52 

6 ( x - 5 ) = 52 - 46 

6 ( x - 5 ) = 6

x - 5 = 6 : 6 

x - 5 = 1 

x = 1 + 5 

x = 6 

Bài 2

a 3x-5=2

=> 3x=7

=> x=7/3

b 46+6(x-5)=52

=> 6(x-5)=6

=> x-5=1

=> x=6 ( tick nhé )

\(\Leftrightarrow2^{x+1}=8\)

=>x+1=3

hay x=2