a)

\(2^{n-1}:2=256\)

\(\Rightarrow2^{n-1}:2=2^8\)

\(\Rightarrow2^{n-1}=2^9\)

\(\Rightarrow n-1=9\)

\(\Rightarrow n=10\)

b)

\(5^n+5^{n-2}=650\)

\(\Rightarrow5^n+5^n:5^2=650\)

\(\Rightarrow5^n+5^n:25=650\)

\(\Rightarrow5^n+5^n.\dfrac{1}{25}=650\)

\(\Rightarrow5^n.\left(1+\dfrac{1}{25}\right)=650\)

\(\Rightarrow5^n.\dfrac{26}{25}=650\)

\(\Rightarrow5^n=625\)

\(\Rightarrow5^n=5^4\)

\(\Rightarrow n=4\)

c)

\(2^{n-3}+2^{n+1}=136\)

\(\Rightarrow2^n.\dfrac{1}{2^3}+2^n.2=136\)

\(\Rightarrow2^n.\left(\dfrac{1}{8}+2\right)=136\)

\(\Rightarrow2^n.\dfrac{17}{8}=136\)

\(\Rightarrow2^n=64\)

\(\Rightarrow2^n=2^6\)

\(\Rightarrow n=6\)

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!
 

ggggggggggggggggggggggggg

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''!

???

\(3^2.3^5.3^n=3^{11}\)

\(\Rightarrow3^7.3^n=3^{11}\)

\(\Rightarrow3^n=3^{11}:3^7\)

\(\Rightarrow3^n=3^4\)

\(\Rightarrow n=4\)

tíc mình nha

Bài 6 :

a) \(\dfrac{625}{5^n}=5\Rightarrow\dfrac{5^4}{5^n}=5\Rightarrow5^{4-n}=5^1\Rightarrow4-n=1\Rightarrow n=3\)

b) \(\dfrac{\left(-3\right)^n}{27}=-9\Rightarrow\dfrac{\left(-3\right)^n}{\left(-3\right)^3}=\left(-3\right)^2\Rightarrow\left(-3\right)^{n-3}=\left(-3\right)^2\Rightarrow n-3=2\Rightarrow n=5\)

c) \(3^n.2^n=36\Rightarrow\left(2.3\right)^n=6^2\Rightarrow\left(6\right)^n=6^2\Rightarrow n=6\)

d) \(25^{2n}:5^n=125^2\Rightarrow\left(5^2\right)^{2n}:5^n=\left(5^3\right)^2\Rightarrow5^{4n}:5^n=5^6\Rightarrow\Rightarrow5^{3n}=5^6\Rightarrow3n=6\Rightarrow n=3\)

Bài 7 :

a) \(3^x+3^{x+2}=9^{17}+27^{12}\)

\(\Rightarrow3^x\left(1+3^2\right)=\left(3^2\right)^{17}+\left(3^3\right)^{12}\)

\(\Rightarrow10.3^x=3^{34}+3^{36}\)

\(\Rightarrow10.3^x=3^{34}\left(1+3^2\right)=10.3^{34}\)

\(\Rightarrow3^x=3^{34}\Rightarrow x=34\)

b) \(5^{x+1}-5^x=100.25^{29}\Rightarrow5^x\left(5-1\right)=4.5^2.\left(5^2\right)^{29}\)

\(\Rightarrow4.5^x=4.25^{2.29+2}=4.5^{60}\)

\(\Rightarrow5^x=5^{60}\Rightarrow x=60\)

c) Bài C bạn xem lại đề

d) \(\dfrac{3}{2.4^x}+\dfrac{5}{3.4^{x+2}}=\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{10}}\)

\(\Rightarrow\dfrac{3}{2.4^x}-\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{x+2}}-\dfrac{5}{3.4^{10}}=0\)

\(\Rightarrow\dfrac{3}{2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)+\dfrac{5}{3.4^2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)=0\)

\(\Rightarrow\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)\left(\dfrac{3}{2}+\dfrac{5}{3.4^2}\right)=0\)

\(\Rightarrow\dfrac{1}{4^x}-\dfrac{1}{4^8}=0\)

\(\Rightarrow\dfrac{4^8-4^x}{4^{x+8}}=0\Rightarrow4^8-4^x=0\left(4^{x+8}>0\right)\Rightarrow4^x=4^8\Rightarrow x=8\)

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