viết thế này thánh hiểu

3^x + 2 + 4.3 +1 = 7.3^6

3^x + 2 + 12 + 1 = 21^6

3^x + 15 = 21^6

ko làm được nữa thì hịu

a) \(4^n=4096\Rightarrow4^n=4^6\Rightarrow n=6\)

b) \(5^n=15625\Rightarrow5^n=5^6\Rightarrow n=6\)

c) \(6^{n+3}=216\Rightarrow6^{n+3}=6^3\Rightarrow n+3=3\Rightarrow n=0\)

d) \(x^2=x^3\Rightarrow x^3-x^2=0\Rightarrow x^2\left(x-1\right)=0\Rightarrow\left[{}\begin{matrix}x=0\\x-1=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

e) \(3^{x-1}=27\Rightarrow3^{x-1}=3^3\Rightarrow x-1=3\Rightarrow x=4\)

f) \(3^{x+1}=9\Rightarrow3^{x+1}=3^2\Rightarrow x+1=2\Rightarrow x=1\)

g) \(6^{x+1}=36\Rightarrow6^{x+1}=6^2\Rightarrow x+1=2\Rightarrow x=1\)

h) \(3^{2x+1}=27\Rightarrow3^{2x+1}=3^3\Rightarrow2x+1=3\Rightarrow2x=2\Rightarrow x=1\)

i) \(x^{50}=x\Rightarrow x^{50}-x=0\Rightarrow x\left(x^{49}-1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x^{49}-1=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0\\x^{49}=1=1^{49}\end{matrix}\right.\)  \(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

4ⁿ  =  4096 

4ⁿ = 2¹²

n = 12

5ⁿ = 15625 

5ⁿ = 5⁶

n   = 6

6ⁿ⁺³ = 216

6ⁿ⁺³ = 2³.3³

6ⁿ⁺³ = 6³

n + 3 = 3

4ⁿ = 4096

4ⁿ = 4⁶

n = 6 (nhận)

Vậy n = 6

--------------------

5ⁿ = 15625

5ⁿ = 5⁶

n = 6 (nhận)

Vậy n = 6

--------------------

4ⁿ⁻¹ = 1024

4ⁿ⁻¹ = 4⁵

n - 1 = 5

n = 6 (nhận)

Vậy n = 6

-------------------

6ⁿ⁺³ = 216

6ⁿ⁺³ = 6³

n + 3 = 3

n = 0  (nhận)

Vậy n = 0

--------------------

x² = x³

x³ - x² = 0

x(x² - 1) = 0

x = 0 (nhận) hoặc x² - 1 = 0

*) x² - 1 = 0

x² = 1

x = 1 (nhận) hoặc x = -1 (loại)

Vậy x = 0; x = 1 

--------------------

3ˣ⁻¹ = 27

3ˣ⁻¹ = 3³

x - 1 = 3

x = 3 + 1

x = 4 (nhận)

Vậy x = 4

---------------------

3ˣ⁺¹ = 9

3ˣ⁺¹ = 3²

x + 1 = 2

x = 2 - 1

x = 1 (nhận)

Vậy x = 1

--------------------

6ˣ⁺¹ = 36

6ˣ⁺¹ = 6²

x + 1 = 2

x = 2 - 1

x = 1 (nhận)

Vậy x = 1

--------------------

3²ˣ⁺¹ = 27

3²ˣ⁺¹ = 3³

2x + 1 = 3

2x = 3 - 1

2x = 2

x = 1 (nhận)

Vậy x = 1

--------------------

x⁵⁰ = x

x⁵⁰ - x = 0

x(x⁴⁹ - 1) = 0

x = 0 (nhận) hoặc x⁴⁹ - 1 = 0

*) x⁴⁹ - 1 = 0

x⁴⁹ = 1

x = 1 (nhận)

Vậy x = 0; x = 1

\(7\cdot3^{x-1}-3^{x+2}=540\)

=>\(7\cdot3^x\cdot\dfrac{1}{3}-3^x\cdot9=540\)

=>\(3^x\left(\dfrac{7}{3}-9\right)=540\)

=>\(3^x\cdot\dfrac{-20}{3}=540\)

=>\(3^x=-540:\dfrac{20}{3}=-540\cdot\dfrac{3}{20}=-27\cdot3=-81\)

=>\(x=log_3\left(-81\right)\)

Bài 9,

6²x73+36x3³=36x73+36x27=36(73+27)=36x100=3600.

197-\([\)6x(5-1)²+2022⁰\(]\):5=197-\([\)6x16+1\(]\):5=197-97:5=197-97/5=888/5.

Bài 10,

21-4x=13

=>4x=21-13=8

=>x=8:4=2.

30:(x-3)+1=4⁵:4³=4²=16

=>30:(x-3)=16-1=15

=>x-3=30:15=2

=>x=2+3=5.

(x-1)³+5x6=38

=>(x-1)³+30=38

=>(x-1)³=38-30=8=2³

=>x-1=2

=>x=3.

1) \(2^8.4.16.32.64.2=2^8.2^2.2^4.2^5.2^6.2=2^{8+2+4+5+6+1}=2^{26}\)

2) \(7.3^x-11=52\Rightarrow7.3^x=52+11=63\)

\(\Rightarrow3^x=63:7=9\Rightarrow3^x=3^2\Rightarrow x=2\)

\(4^{10\left(x+5\right)}=4^{12}\Rightarrow10\left(x+5\right)=12\)

\(\Rightarrow10x+50=12\Rightarrow10x=12-50=-38\)

\(\Rightarrow x=-38:10=-\dfrac{38}{10}=-\dfrac{19}{5}\)

\(7x-2x=6^{17}:6^{15}+2^8:2^6\)

\(\Rightarrow5x=6^2+2^2\Rightarrow5x=36+4=40\)

\(\Rightarrow x=40:5=8\)

\(3^{2x-1}=27\Rightarrow3^{2x-1}=3^3\Rightarrow2x-1=3\)

\(\Rightarrow2x=4\Rightarrow x=4:2=2\)

1) 2⁸. 4 . 16 . 32 . 64

= 2⁸. 2². 2⁴. 2⁵. 2⁶

= 2²⁵

2) 7 . 3^x - 11 = 52                                  4¹⁰ .(x + 5) = 4¹²

⇒        7 . 3^x = 52 + 11                      ⇒           x + 5 = 4¹² : 4¹⁰

⇒        7 . 3^x = 63                              ⇒           x + 5 = 4²

⇒             3^x = 63 : 7                         ⇒           x + 5 = 16

⇒             3^x = 9                                ⇒                 x = 16 - 5

⇒             3^x = 3²                               ⇒                x = 11

⇒              x = 2                                    Vậy x = 11

   Vậy x = 2

Lời giải:
a. $x^3=4^3\Rightarrow x=4$

b. $x^2=49=7^2=(-7)^2$

$\Rightarrow x=7$ hoặc $x=-7$

c. $x^3+1=28$

$x^3=28-1=27=3^3$

$\Rightarrow x=3$

d. $2^x=16=2^4$

$\Rightarrow x=4$

e. $2^4.2^x=2^6$

$\Rightarrow 2^{4+x}=2^6$

$\Rightarrow 4+x=6$

$\Rightarrow x=2$

g.

$5^x=25.5^3=5^2.5^3=5^5$

$\Rightarrow x=5$

Lần sau bạn lưu ý viết đề bằng công thức toán (biểu tượng $\sum$ góc trái khung soạn thảo) để đề được rõ ràng hơn nhé.

1. \(6x^3-8=40\\ 6x^3=48\\ x^3=8\\ \Rightarrow x=2\)Vậy x = 2

2. \(4x^5+15=47\\ 4x^5=32\\ x^5=8\\ \Rightarrow x\in\varnothing\left(\text{vì }x\in N\right)\)Vậy x ∈ ∅

3. \(2x^3-4=12\\ 2x^3=16\\ x^3=8\\ \Rightarrow x=2\)Vậy x = 2

4. \(5x^3-5=0\\ 5x^3=5\\ x^3=1\\ \Rightarrow x=1\)Vậy x = 1

5. \(\left(x-5\right)^{2016}=\left(x-5\right)^{2018}\\ \Rightarrow\left[{}\begin{matrix}x-5=0\\x-5=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=5\\x=6\end{matrix}\right.\)Vậy \(x\in\left\{5;6\right\}\)

6. \(\left(3x-2\right)^{20}=\left(3x-1\right)^{20}\\ \Rightarrow3x-2=3x-1\\ 3x-3x=2-1\\ 0=1\left(\text{vô lí}\right)\)Vậy x ∈ ∅

7. \(\left(3x-1\right)^{10}=\left(3x-1\right)^{20}\\ \left(3x-1\right)^{10}=\left[\left(3x-1\right)^2\right]^{10}\\ \Rightarrow\left(3x-1\right)^2=3x-1\\ \left(3x-1\right)^2-\left(3x-1\right)=0\\ \left(3x-1\right)\left[\left(3x-1\right)-1\right]=0\\ \left(3x-1\right)\left(3x-2\right)=0\\ \Rightarrow\left[{}\begin{matrix}3x-1=0\\3x-2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}3x=1\\3x=2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{1}{3}\left(\text{loại vì }x\in N\right)\\x=\frac{2}{3}\left(\text{loại vì }x\in N\right)\end{matrix}\right.\)Vậy x ∈ ∅

8. \(\left(2x-1\right)^{50}=2x-1\\ \left(2x-1\right)^{50}-\left(2x-1\right)=0\\ \left(2x-1\right)\left[\left(2x-1\right)^{49}-1\right]=0\\ \Rightarrow\left[{}\begin{matrix}2x-1=0\\\left(2x-1\right)^{49}=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=1\\2x-1=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\frac{1}{2}\left(\text{loại vì }x\in N\right)\\x=1\left(t/m\right)\end{matrix}\right.\)Vậy x = 1

9. \(\left(\frac{x}{3}-5\right)^{2000}=\left(\frac{x}{3}-5\right)^{2008}\\ \left(\frac{x}{3}-5\right)^{2008}-\left(\frac{x}{3}-5\right)^{2000}=0\\ \left(\frac{x}{3}-5\right)^{2000}\left[\left(\frac{x}{3}-5\right)^8-1\right]=0\\ \Rightarrow\left[{}\begin{matrix}\left(\frac{x}{3}-5\right)^{2000}=0\\\left(\frac{x}{3}-5\right)^8=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}\frac{x}{3}-5=0\\\frac{x}{3}-5=1\\\frac{x}{3}-5=-1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}\frac{x}{3}=5\\\frac{x}{3}=6\\\frac{x}{3}=4\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\cdot3=15\\x=6\cdot3=18\\x=4\cdot3=12\end{matrix}\right.\)Vậy \(x\in\left\{15;18;12\right\}\)

\(1.6x^3-8=40\\ \Leftrightarrow6x^3=48\\ \Leftrightarrow x^3=8\Leftrightarrow x^3=2^3=\left(-2\right)^3\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)

Vậy \(x\in\left\{2;-2\right\}\)

\(2.4x^3+15=47\) (T nghĩ đề là mũ 3)

\(\Leftrightarrow4x^3=32\Leftrightarrow x^3=8=2^3=\left(-2\right)^3\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)

Vậy \(x\in\left\{2;-2\right\}\)

Câu 3, 4 tương tự nhé.

\(5.\left(x-5\right)^{2016}=\left(x-5\right)^{2018}\\ \Leftrightarrow\left(x-5\right)^{2018}-\left(x-5\right)^{2016}=0\\ \Leftrightarrow\left(x-5\right)^{2016}\left[\left(x-5\right)^2-1\right]=0\\ \Leftrightarrow\left(x-5\right)^{2016}\left(x-5-1\right)\left(x-5+1\right)=0\\ \Leftrightarrow\left(x-5\right)^{2016}\left(x-6\right)\left(x-4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}\left(x-5\right)^{2016}=0\\x-6=0\\x-4=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x-5=0\\x=6\\x=4\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=5\\x=6\\x=4\end{matrix}\right.\)

Vậy \(x\in\left\{4;5;6\right\}\)

  Bài 1:

2^\(x\) = 4

2\(^x\) = 2²

 \(x=2\)

Vậy \(x=2\)

Bài 2:

2\(^x\) = 8

2\(^x\) = 2³

\(x=3\)

Vậy \(x=3\)

Bài 3

2\(^x\) = 16

2\(^x\) = 2⁴

  \(x=4\)

Vậy \(x=4\)

Bài 1 :

a) 2^x-64=2⁶

=> 2^x-2⁶=2⁶

2^x=2⁶+2⁶ (2⁶⁺⁶)

2^x = 2¹²

<=> x = 12

b) 2^x:16=128

=> 2^x.2⁴ = 2⁷

2^x = 2⁷:2⁴ (2^7-4)

2^x = 2³

<=> x=3

Bài 2 :

b) A= 8² = (2³)² = 2⁶  

B= 2⁶

=> A = B ( 2⁶=2⁶ )

c) A= 3⁵ = 243

B = 2⁸ = 256

=> A < B ( 243 < 256 )