a) \(3^x.3=243\)

\(\Rightarrow3^{x+1}=3^5\)

\(\Rightarrow x+1=5\)

\(\Rightarrow x=4\)

b) \(2^x.7=56\)

\(2^x=56:7\)

\(\Rightarrow2^x=8\)

\(\Rightarrow2^x=2^3\)

\(\Rightarrow x=3\)

\(3^x.3=243\)

\(\Rightarrow3^x=81\)

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

\(\Rightarrow x=4\)

\(2^x.7=56\)

\(\Rightarrow2^x=56:7\)

\(\Rightarrow2^x=8\)

\(\Rightarrow2^x=2^3\)

\(\Rightarrow x=3\)

\(a,\)  \(3^x.3=243\)

\(\Rightarrow3^x.3=3^5\)

\(\Rightarrow3^x=3^5:3\)

\(\Rightarrow3^x=3^{5-1}\)

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

\(\Rightarrow x=4\)

Vậy \(x=4\)

\(b,\) \(2^x.7=56\)

\(\Rightarrow2^x=56:7\)

\(\Rightarrow2^x=8\)

\(\Rightarrow2^x=2^3\)

\(\Rightarrow x=3\)

Vậy \(x=3\)

`#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) \(3^x+3^{x+2}=810\)

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

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

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

\(\Rightarrow3^x=81\)

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

\(\Rightarrow x=4\)

a) 3^x.3=243

=> 3^x= 81 =>  x= 4

b) 2^x.7=56

=> 2^x= 8 => x= 3

c) x³=8²

=> x³= 64 => x= 4

d) x²⁰=x thì x chỉ bằng 1 mà thôi, vì 1 mũ mấy cũng bằng 1

k nha!!! ><

Chúc bn hc tốt ^3^

Ý mik là k chứ hk phải k nha

mik lộn

Chúc bn hc tốt ^^^^^^

a,3^x.3=243

3^x=81

3^x=3⁴

x=4

vậy x=4

b,2^x.7=56

2^x=8

2^x=2³

x=3

Vậy x=3

x³=8²

x³=64

x³=4³

x=4

Vậy x=4

x²⁰=x

\(\Rightarrow\)x=1

Vậy x=1

a,9<3^x<3⁹.3^-2

\(\Leftrightarrow3^2< 3< 3^7\)

\(\Rightarrow S=\left\{3;4;5;6\right\}\)

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

\(\Rightarrow3^{2x+1}=3^5\)

\(\Rightarrow2x+1=5\)

\(\Rightarrow2x=5-1\)

\(\Rightarrow2x=4\)

\(\Rightarrow x=4:2\)

\(\Rightarrow x=2\)

\(3^2x+1=243\)

\(9x=243-1\)

\(9x=242\)

\(x=242:9\)

\(\Rightarrow x=\dfrac{242}{9}\)

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

a/ 2^x+2 + 2^x = 144

=> 2^x (2² + 1) = 144

=> 2^x = 144/5

=> k có giá trị nào của x thỏa biểu thức trên

b/ (2x + 1)³ = 243

=> đề sai

a: \(\Leftrightarrow\left(2x-3;y+5\right)\in\left\{\left(1;20\right);\left(2;10\right);\left(4;5\right);\left(5;4\right);\left(10;2\right);\left(20;1\right)\right\}\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x-3=1\\y+5=20\end{matrix}\right.\Leftrightarrow\left(x,y\right)\in\left(2;15\right)\)

b: \(\Leftrightarrow\left(x-7;y+1\right)\in\left\{\left(1;18\right);\left(2;9\right);\left(3;6\right);\left(6;3\right);\left(9;2\right);\left(18;1\right)\right\}\)

hay \(\left(x,y\right)\in\left\{\left(8;17\right);\left(9;8\right);\left(10;5\right);\left(13;2\right);\left(16;1\right);\left(25;0\right)\right\}\)

A) \(3^x\cdot3=243\)

\(\Leftrightarrow3^x=243:3=81\)

\(\Leftrightarrow3^x=3^4\)

\(\Leftrightarrow x=4\)

B) \(2^x-15=17\)

\(\Leftrightarrow2^x=17+15\)

\(\Leftrightarrow2^x=32\)

\(\Leftrightarrow2^x=2^5\)

\(\Leftrightarrow x=5\)

C) \(\left(x-1\right)^2-7=42\)

\(\Leftrightarrow\left(x-1\right)^2=49\)

\(\Rightarrow\orbr{\begin{cases}x-1=7\\x-1=-7\end{cases}\Rightarrow\orbr{\begin{cases}x=8\\x=-6\end{cases}}}\)

Câu a thì có nhiều cách nhưng mình chỉ làm 1 cách thôi nhé

a) 3^x . 3 = 243

=> 3^x . 3¹ = 3⁵

3^x = 3⁵ : 3¹

3^x = 3^5-1

3^x = 3⁴

<=> x = 4

b) 2^x - 15 = 17

2^x = 17 - 15

2^x = 2

<=> 2^x = 2¹ => x = 1

c) (x-1)² - 7 = 42

(x-1)² = 42 + 7

(x-1)² = 49

x-1 = 49 = 7.7

<=> x-1 = 7

x = 7 + 1

x = 8