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

a, 3^x . 3 = 243

3^x+1 = 3⁵ 

=> x + 1 = 5 => x = 4

b, 7^x . 49  = 7²⁷

7^x . 7² = 7²⁷

7^x+2 = 7²⁷

=> x + 2 = 27 => x = 25

c, 5^x+1 = 125

5^x+1 = 5³

=> x + 1 = 3 => x = 2

a) 219-7x-7=100

212-7x=100

7x=112

x=16

các câu còn lại cứ thế mà làm

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 \(x=3\)

2^x = 64

⇒ 2^x = 2⁶

⇒ x = 6.

7^x = 7¹⁰ : 7⁵

⇒ 7^x = 7⁵

⇒ x = 5.

3^x = 3¹⁵ : 243

⇒ 3^x = 3¹⁵ : 3⁵

⇒ 3^x = 3¹⁰

⇒ x = 10.

\(2^x=64=2^6\Rightarrow x=6\\ ---\\ 7^x=7^{10}:7^5=7^5\Rightarrow x=5\\ ----\\ 3^x=3^{15}:243=3^{15}:3^5=3^{10}\Rightarrow x=10\)

2^x= 64 => x = 6

7^x= 7¹⁰: 7⁵ => x=10 - 5 =5

3^x==3¹⁵: 243 = 3¹⁵- 3⁵=> x = 15-5 =10

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

sai đề rồi

\(\Leftrightarrow3^x\cdot3=243\)

hay x=4

3^x.3=243

<=>3^x.3¹=243

Mà: 3⁵=243

=> 3^x.3¹=3⁵

=>3^x= 3^5-1

=>3^x=3⁴

=> x=4

Ta có : 3^x . 3 =243
          =>3^x = 243 : 3 = 81
          =>3^x = 3^4
          =>x = 4

(3^x)^2=1/243.3^3

(3^x)^2=1/9

3x=1/3 hoặc 3x=-1/3

Suy ra x=1/9 hoặc x=-1/9