a)

\(3^{n+1}+5.3^{n-2}=2592\)

\(\Rightarrow3^{n+1}+5.3^{n+1-3}=2592\)

\(\Rightarrow3^{n+1}+\dfrac{1}{27}.5.3^{n+1}=2592\)

\(\Rightarrow3^{n+1}+\dfrac{5}{27}.3^{n+1}=2592\)

\(\Rightarrow3^{n+1}.\left(\dfrac{5}{27}+1\right)=2592\)

\(\Rightarrow3^{n+1}.\dfrac{32}{27}=2592\)

\(\Rightarrow3^{n+1}=2187\)

\(\Rightarrow3^{n+1}=3^7\)

\(\Rightarrow n+1=7\)

\(\Rightarrow n=6\)

b)

\(3^{n+2}.5.3^{n-1}=864\)

\(\Rightarrow3^{n+2}+\dfrac{1}{27}.5.3^{n+2}=864\)

\(\Rightarrow3^{n+2}\left(\dfrac{5}{27}+1\right)=864\)

\(\Rightarrow3^{n+2}.\dfrac{32}{27}=864\)

\(\Rightarrow3^{n+2}=729\)

\(\Rightarrow3^{n+2}=3^6\)

\(\Rightarrow n+2=6\)

\(\Rightarrow n=4\)

a. 

\(5^n+5^{n+2}=650\) 

\(5^n\left(1+5^2\right)=650\) 

\(5^n\left(1+25\right)=650\) 

\(5^n\cdot26=650\) 

\(5^n=650:26\) 

\(5^n=25\) 

\(5^n=5^2\Rightarrow n=2\) 

b. 

\(3^{n+3}+5\cdot3^n=864\) 

\(3^n\left(3^3+5\right)=864\) 

\(3^n\left(27+5\right)=864\) 

\(3^n\cdot32=864\) 

\(3^n=864:32\) 

\(3^n=27\) 

\(3^n=3^3\Rightarrow n=3\)

a) 5ⁿ + 5ⁿ⁺² = 650

=> 5ⁿ + 5ⁿ . 5² = 650

=> 5ⁿ (1 + 5²) = 650

=> 5ⁿ . 26 = 650

=> 5ⁿ = 25

=> n = 2

b) 3^{n+ 3} + 5.3ⁿ = 864

=> 3ⁿ . 3³ + 5.3ⁿ = 864

=> 3ⁿ(3³ + 5) = 864

=> 3ⁿ . 32 = 864

=> 3ⁿ = 27

=> n = 3

a, 

5ⁿ + 5^{n + 2} = 650

=> 5ⁿ + 5ⁿ.5² = 650

=> 5ⁿ(1 + 5²) = 650

=> 5ⁿ.26 = 650

=> 5ⁿ = 25

=> n = 2

a) 5ⁿ +5ⁿ⁺² = 650

5ⁿ + 5ⁿ.5² = 650

5ⁿ.(1+25 ) = 650

5ⁿ.26= 650

5ⁿ = 25 = 5² 

=> n = 2

b) 3ⁿ⁺³ +5.3ⁿ = 864

3ⁿ.3³ +5.3ⁿ = 864

3ⁿ.(3³+5) = 864

3ⁿ.32 = 864

3ⁿ = 27 = 3³

=> n = 3

các bài cn lại bn dựa vào mak lm nha!
 

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a) 5ⁿ + 5ⁿ⁺² = 650   

=> 5ⁿ+5ⁿ⁺²=5⁴ +5²

=> n+n+2 = 4+2

=>2n +2 = 6

=> n=2

  b) 3ⁿ + 5.3ⁿ= 864 

=> 3ⁿ .(1+5) = 864

=> 3ⁿ = 864 :6

=> 3ⁿ =144

=> 3ⁿ =3²+3³+3⁴-3

=> n=2+3+4-3=6

 c ) 5ⁿ⁺³ - 5ⁿ⁺¹= (125)⁴ . 120

 => 5ⁿ⁺³ - 5^{n+ =} 5¹². ( 5^3 -5)

=> n+3 -n = 12.2

=> 3=14 ( vô lí )

=> không tồn tại n

Kunzy Nguyễn: Mik ko có ý chê bạn đâu nhưng mà câu a mik thấy bạn giải có chút gọi là ''sai''!

e) 3ⁿ⁺² + 5.3^{n + 1} = 216

=> 3ⁿ . 3² + 5.3ⁿ . 3¹ = 216

=> 3ⁿ . 9 + 15.3ⁿ = 216

=> 3ⁿ ( 9 + 15) = 216

=> 3ⁿ . 24 = 216

=> 3ⁿ = 9

=> n = 2

f) 5^{n + 1} - 5^{n - 1} = 125⁴ . 2³ . 37

=> 5ⁿ . 5 - 5ⁿ  . 1/5 = 125⁴ . 2³ . 37

=> 5ⁿ ( 5 - 1/5) = 125⁴ . 2³ . 37

=> 5ⁿ . 24/5 = 125⁴ . 2³ . 37

=> n không thỏa mãn

a,\(3^{n+2}+5.3^{n+1}=216\)

\(3^n.9+5.3^n.3=216\)

\(3^n\left(9+5.3\right)=216\)

\(3^n.24=216\)

\(3^n=9\Rightarrow n=2\)

a) 5ⁿ . 5^{n + 2} = 650

=> 5ⁿ + 5ⁿ . 5² = 650

=> 5ⁿ . (1 + 5²) = 650

=> 5ⁿ . 26          = 650

=> 5ⁿ                  = 650 : 26 

=> 5ⁿ                  = 25

=> 5ⁿ                  = 5²

=>   n                 = 2

b) 3^{n + 3} + 5.3ⁿ = 864

=> 3ⁿ . 3³ + 5.3ⁿ = 864

=> 3ⁿ . (3³ + 5)   = 864

=> 3ⁿ . 32           = 864

=> 3ⁿ                  = 864 : 32

=> 3ⁿ                  = 27

=> 3ⁿ                  = 3³

=>   n                  = 3

ý b nha bạn

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