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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kkkkk

a) \(A=2+2^2+...+2^{2024}\)

\(2A=2^2+2^3+...+2^{2025}\)

\(2A-A=2^2+2^3+...+2^{2025}-2-2^2-...-2^{2024}\)

\(A=2^{2025}-2\) 

b) \(2A+4=2n\)

\(\Rightarrow2\cdot\left(2^{2025}-2\right)+4=2n\)

\(\Rightarrow2^{2026}-4+4=2n\)

\(\Rightarrow2n=2^{2026}\)

\(\Rightarrow n=2^{2026}:2\)

\(\Rightarrow n=2^{2025}\) 

c) \(A=2+2^2+2^3+...+2^{2024}\)

\(A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{2023}+2^{2024}\right)\)

\(A=2\cdot3+2^3\cdot3+...+2^{2023}\cdot3\)

\(A=3\cdot\left(2+2^3+...+2^{2023}\right)\)

d) \(A=2+2^2+2^3+...+2^{2024}\)

\(A=2+\left(2^2+2^3+2^4\right)+\left(2^5+2^6+2^7\right)+...+\left(2^{2022}+2^{2023}+2^{2024}\right)\)

\(A=2+2^2\cdot7+2^5\cdot7+...+2^{2022}\cdot7\)

\(A=2+7\cdot\left(2^2+2^5+...+2^{2022}\right)\)

Mà: \(7\cdot\left(2^2+2^5+...+2^{2022}\right)\) ⋮ 7

⇒ A : 7 dư 2 

9

a) \(11^n=1331\)

\(\Rightarrow11^n=11^3\)

\(\Rightarrow n=3\)

b) \(n^3=125\)

\(\Rightarrow n^3=5^3\)

\(\Rightarrow n=5\)

c) \(5^4=n\)

\(\Rightarrow625=n\)

\(\Rightarrow n=625\)

d) \(\left(n+1^2\right)=9\)

\(\Rightarrow n+1=9\)

\(\Rightarrow n=9-1\)

\(\Rightarrow n=8\)

a) 11^n = 1331

⇒ 11^n = 11^3

⇔ n = 3

b) n^ 3 = 125

⇒ n^3 = 5^3

⇔ n = 5

c) 5^4 = n 

⇒ n = 625

d) ( n + 1^2 ) = 9

⇒ ( n + 1 ) = 9

⇒ n = 8 

\(2^{2n}+1=32\)

\(\Rightarrow2^{2n}+1=2^5\)

\(\Rightarrow2^{2n}+1=5\)

\(\Rightarrow2n=4\)

\(\Rightarrow n=2\)

a) \(2^n:4=16\Rightarrow2^n:2^2=2^4\Rightarrow2^{n-2}=2^4\Rightarrow n-2=4\Rightarrow n=6\)

b) \(6\cdot2^n+3\cdot2^n=9\cdot2^9\)

=> \(\left(6+3\right)\cdot2^n=9\cdot2^9\)

=> \(9\cdot2^n=9\cdot2^9\Rightarrow n=9\)

c) \(3^n:3^2=243\)

=> \(3^{n-2}=3^5\)

=> n - 2 = 5 => n = 7

d) 25 < 5ⁿ < 3125

=> 5² < 5ⁿ < 5⁵

=> n \(\in\){3;4}

em tính 3A đi

sao đok e lấy 3A-A là đc 2A

tiếp theo chéc e cx bik lm rồi nhỉ, tự lm cho quẹn

A=3+3^2+3^3+........+3^100

3A=3^2+3^3+........+3^101

3A-A=(3^2+3^3+........+3^101)-(3+3^2+3^3+........+3^100)

2A=3^101-3

suy ra: n=3^101-3+3=3^101

**** cho chị nhé! (bài này dễ, em cố gắng luyện nhìu nhé, lm hoài sẽ cok nhìu dạng nâng cao khó hơn)

Mần^o^

dap an la n =101

a)n+5 chia hết cho n-1

=>n-1+6 chia hết cho n-1 

=> 6 chia hết cho n-1 hay n-1EƯ(6)={1;2;3;6}

=>nE{2;3;4;7}

b)3n+1 chia hết cho n+1

3n+3-2 chia hết cho n+1

3(n+1)-2 chia hết cho n+1

=>2 chia hết cho n+1 hay n+1EƯ(2)={1;2}

nE{0;1}

a) \(\frac{16}{2^n}=2\)

=> 2.2ⁿ = 16

=> 2¹⁺ⁿ = 2⁴

=> 1 + n = 4

=> n = 4 - 1

=> n = 3

Vậy n = 3

b) \(\frac{\left(-3\right)^n}{81}=-27\)

=> (-3)ⁿ = -27.81

=> (-3)ⁿ = -3³.3⁴

=> (-3)ⁿ = (-3)⁷

=> n = 7

Vậy n = 7

c) 8ⁿ : 2ⁿ = 4

=> (8 : 2)ⁿ = 4

=> 4ⁿ = 4¹

=> n = 1

Vậy n = 1