1) 4ⁿ = 4096

<=> 4ⁿ = 4⁶

<=> n = 6

=> x = 6

2) 5ⁿ = 15625

<=> 5ⁿ = 5⁶

<=> n = 6

=> x = 6

3) 6^{n + 3} = 216

<=> 6^{n + 3} = 6³

<=> n + 3 = 0

<=> n = 0

=> n = 0

4) 4^{n - 1} = 1024

<=> 4^{n - 1} = 4⁵

<=> n - 1 = 5

<=> n = 6

=> n = 6

Đặt tổng trên = A

\(A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{4096}+\frac{1}{8192}\)

\(A.2=2+1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2048}+\frac{1}{4096}\)

\(A.2-A=\left(2+1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2048}+\frac{1}{4096}\right)-\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{4096}+\frac{1}{8192}\right)\)

\(A=2-\frac{1}{8192}=\frac{16383}{8192}\)
 

Đặt A = 1 + 1/2 + 1/4 + 1/8 + ... + 1/4096 + 1/8192

2A = 2 + 1 + 1/2 + 1/4 + ... + 1/2048 + 1/4096

2A - A = (2 + 1 + 1/2 + 1/4 + ... + 1/2048 + 1/4096) - (1 + 1/2 + 1/4 + 1/8 +... + 1/4096 + 1/8192)

A = 2 - 1/8192

A = 16383/8192

A = 1+2+4+8+...+8192

A = 2 0 + 2 1 + 2 2 + 2 3 +...+2 13

2A = 2 1+2 2+2 3+2 4+...+2 14

2A ‐ A = 2 14 ‐ 2 0

=> A = 2 14 ‐ 1

= 16781312 + 1 = 16781313 

k tớ nhé 

k ết bạn nha 

li -ke cho tớ thật nhiều tuần sau li -ke lại cho 

Đặt A=1/2+1/4+1/8+1/16+1/32+...+1/2048+1/4096

\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{12}}\)

\(2A=2\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{12}}\right)\)

\(2A=1+\frac{1}{2}+...+\frac{1}{2^{11}}\)

\(2A-A=\left(1+\frac{1}{2}+...+\frac{1}{2^{11}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{12}}\right)\)

\(A=1-\frac{1}{2^{12}}\)

a) n = 4 ; n = 5

b) n = 6 ; n = 6

c) n = 0 ; n = 6

a>2^n=16=>2^n=2^4 =>n=4

   3^n=243=> 3^n=3^5 =>n=5

 b>4^n=4096 =>4^n=4^6=>n=6

     5^n=15625 =>5^n=5^6 =>n=6

c>6^n+3=216 =. 6^n+3=6^3 =>n+3=3

                                              n=0

   4^n-1=1024 =>4^n-1=4^5 =>n-1=5

                                             n=4

Chuc ban vao nam hoc dc nhieu may man!!

2^n=2^4

3^n=3^5

4^n=4^6

5^n=5^6

6^n+3=6^0+3

4^n-1=4^6-1

n=4

n=5

n=6

n=6

n=0

n=6

k cho minh nha

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