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

\(^{3^{x+2-3^x}=216}\) á !?!

3^x+2-3^x=216

3^x.3²-3^x=216

3^x(3²-1)=216

\(\Rightarrow\)3^x=216:8=27

\(\Rightarrow\)3^x=3³

Vậy x = 3

lấy một ở đâu ra mình không hiểu lắm

Sửa đề:

\(3^{x+1}+3^x\cdot5=216\\\Rightarrow 3^x\cdot 3+3^x\cdot5=216\\\Rightarrow3^x\cdot(3+5)=216\\\Rightarrow3^x\cdot8=216\\\Rightarrow3^x=216:8\\\Rightarrow3^x=27\\\Rightarrow3^x=3^3\\\Rightarrow x=3\)

Kiểm tra lại bài nhé bạn.

các bạn giúp mik vs

\(\left(-216\right):9+7^5:7^3-\left(-4\right)^2.5\)

\(\Leftrightarrow\left(-24\right)+7^2-16\)

\(\Leftrightarrow\left(-24\right)+49-16\)

\(\Leftrightarrow25-16\)

\(\Leftrightarrow9\)

what are doing?

I am doing homework

what are you doing??????

\(318-5\left(x-64\right)=103\)

\(\Rightarrow5\left(x-64\right)=318-103\)

\(\Rightarrow5\left(x-64\right)=215\)

\(\Rightarrow x-64=43\)

\(\Rightarrow x=43+64\)

\(\Rightarrow x=107\)

_____________

\(4^x\cdot5+216=296\)

\(\Rightarrow4^x\cdot5=296-216\)

\(\Rightarrow4^x\cdot5-80\)

\(\Rightarrow4^x=16\)

\(\Rightarrow4^x=4^2\)

\(\Rightarrow x=2\)

___________

\(376-6^x:3=364\)

\(\Rightarrow6^x:3=376-364\)

\(\Rightarrow6^x:3=12\)

\(\Rightarrow6^x=36\)

\(\Rightarrow6^x=6^2\)

\(\Rightarrow x=2\)

___________

\(\left(4x-1\right)^2=121\)

\(\Rightarrow\left(4x-1\right)^2=11^2\)

\(\Rightarrow\left[{}\begin{matrix}4x-1=11\\4x-1=-11\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}4x=12\\4x=-10\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{5}{2}\end{matrix}\right.\)

107

2

2

TH1: 3; TH2: -5/2

chắc sai đề bn ơi.

4 x 2^x=128

2^x=128 :4=32

Mà 2⁵=32

=>x=5

4+2⁵=128