Thiếu điều kiện rồi em!

a) 3n + 6 = 3n - 1 + 7

Để (3n + 6) ⋮ (3n - 1) thì 7 ⋮ (3n - 1)

⇒ 3n - 1 ∈ Ư(7) = {-7; -1; 1; 7}

⇒ 3n ∈ {-6; 0; 2; 8}

⇒ n ∈ {-2; 0; 2/3; 8/3}

b) Để (7n + 8) ⋮ n thì 8 ⋮ n

⇒ n ∈ {-8; -4; -2; -1; 1; 2; 4; 8}

a) \(5^{300}\) và \(3^{500}\)

\(\Rightarrow5^{300}< 3^{555}\)

b) \(2^{400}\) và \(4^{200}\)

\(\Rightarrow2^{400}=4^{200}\)

c) \(5^{300}\) và \(3^{453}\)

\(\Rightarrow5^{300}>3^{453}\)

Mai và Lan trực lại sau mỗi:

\(36:2=18\left(ngày\right)\)

Vậy lần trực thứ 3 Lan và Mai cách ngày trực đầu tiên:

\(18\cdot3=54\left(ngày\right)\)

Đáp số: 54 ngày

34

a) \(3119\cdot121-3119\cdot11\cdot11\)

\(=3119\cdot121-3119\cdot\left(11\cdot11\right)\)

\(=3119\cdot121-3119\cdot121\)

\(=3119\left(121-121\right)\)

\(=0\)

b) \(24\cdot\left(123\cdot87\right)+\left(87\cdot123\right)\cdot76\)

\(=\left(123\cdot87\right)\cdot\left(76+24\right)\)

\(=\left(123\cdot87\right)\cdot100\)

\(=1070100\)

\(13^4\cdot16^2=13\cdot13\cdot13\cdot13\cdot16\cdot16\)

\(=13\cdot13\cdot13\cdot13\cdot4\cdot4\cdot4\cdot4\)

\(=\left(13\cdot4\right)\left(13\cdot4\right)\left(13\cdot4\right)\left(13\cdot4\right)\)

\(=52\cdot52\cdot52\cdot52\)

\(=52^4\)

k nha

Vẫn có nha em.

\(\left(x+1\right)^2=25\)

\(\Rightarrow\left(x+1\right)^2=\left(\pm5\right)^2\)

\(\Rightarrow\left[{}\begin{matrix}x+1=5\\x+1=-5\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=5-1\\x=-5-1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=4\\x=-6\end{matrix}\right.\)

\(\left(x+1\right)\cdot2=25\)

\(2x+2=25\)

\(2x=25-2=23\)

\(x=23:2=11,5\)

`#3107`

\(3^{8x+4}=81^{x+3}\\ \Rightarrow3^{8x+4}=\left(3^4\right)^{x+3}\\ \Rightarrow3^{8x+4}=3^{4x+12}\\ \Rightarrow8x+4=4x+12\\ \Rightarrow8x-4x=12-4\\ \Rightarrow4x=8\\ \Rightarrow x=8\div4\\ \Rightarrow x=2\\ \text{Vậy, x = 2.}\)

Lời giải:

$3^{8x+4}=81^{x+3}$

$3^{8x+4}=(3^4)^{x+3}$

$3^{8x+4}=3^{4(x+3)}$

$\Rightarrow 8x+4=4(x+3)$
$\Rightarrow 2x+1=x+3$

$\Rightarrow x=2$

\(3^2\cdot\left(x+4\right)-5^2=5\cdot22\)

\(\Rightarrow9\cdot\left(x+4\right)-25=110\)

\(\Rightarrow9\cdot\left(x+4\right)=110+25\)

\(\Rightarrow9\cdot\left(x+4\right)=135\)

\(\Rightarrow x+4=\dfrac{135}{9}\)

\(\Rightarrow x+4=15\)

\(\Rightarrow x=15-4\)

\(\Rightarrow x=11\)

`#3107`

\(3^2\cdot\left(x+4\right)-5^2=5\cdot22\\ \Rightarrow3^2\left(x+4\right)=5\cdot22+5^2\\ \Rightarrow9\left(x+4\right)=110+25\\ \Rightarrow9\left(x+4\right)=135\\ \Rightarrow x+4=135\div9\\ \Rightarrow x+4=15\\ \Rightarrow x=15-4\\ \Rightarrow x=11\)

Vậy, `x = 11.`