\(3^{8x+4}=81^{x+3}\)

\(\Rightarrow3^{8x+4}=\left(3^4\right)^{x+3}\)

\(\Rightarrow3^{8x+4}=3^{4\left(x+3\right)}\)

\(\Rightarrow8x+4=4x+12\)

\(\Rightarrow8x-4x=12-4\)

\(\Rightarrow4x=8\)

\(\Rightarrow x=\dfrac{8}{4}\)

\(\Rightarrow x=2\)

a) Lâm trường trồng số cây phi lao là:

\(2\times11235=22470\) (cây)

b) Tổng số gây bạch đằng và phi lao lâm trường trồng được là;
\(22470+11235=33705\) (cây)

Đáp số: ...

\(B=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{2004}\right)\)

\(B=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot...\cdot\dfrac{2003}{2004}\)

\(B=\dfrac{1\cdot2\cdot3\cdot...\cdot2003}{2\cdot3\cdot4\cdot...\cdot2004}\)

\(B=\dfrac{1}{2004}\)

a) \(A=\left\{34;124;128\right\}\)

b) \(B=\left\{315;483\right\}\)

c) \(C=\left\{315\right\}\)

\(2\cdot3^x=10\cdot3^{12}+7\cdot27^4\)

\(\Rightarrow2\cdot3^x=10\cdot3^{12}+7\cdot3^{12}\)

\(\Rightarrow2\cdot3^x=3^{12}\cdot\left(10+7\right)\)

\(\Rightarrow2\cdot3^x=3^{12}\cdot17\)

Xem lại đề

Ta có: \(\dfrac{x^2}{-2}=-8\)
\(\Rightarrow x^2=-8\cdot-2=16\Rightarrow\left[{}\begin{matrix}x=4\\x=-4\end{matrix}\right.\)

Khi x=4:

\(B=-\left(4+1\right)^2+\dfrac{1}{2}\cdot\left(-3-3\right)^3=-25\)

Khi x=-4:

\(B=-\left(-4+1\right)^2+\dfrac{1}{2}\cdot\left(-3-3\right)^3=-117\)

a) \(x-\dfrac{3}{4}=6\times\dfrac{3}{8}\)

\(x-\dfrac{3}{4}=\dfrac{9}{4}\)

\(x=\dfrac{9}{4}+\dfrac{3}{4}\)

\(x=3\)

b) \(\dfrac{7}{8}:x=3-\dfrac{1}{2}\)

\(\dfrac{7}{8}:x=\dfrac{5}{2}\)

\(x=\dfrac{7}{8}:\dfrac{5}{2}\)

\(x=\dfrac{7}{20}\)

c) \(x+\dfrac{1}{2}\times\dfrac{1}{3}=\dfrac{3}{4}\)

\(x+\dfrac{1}{6}=\dfrac{3}{4}\)

\(x=\dfrac{3}{4}-\dfrac{1}{6}\)

\(x=\dfrac{7}{12}\)

Đặt: \(d=ƯCLN\left(5m+1,4m+1\right)\)

Nên:

5m + 1 chia hết cho d và 4m + 1 chia hết cho d

4.(5m + 1) chia hết cho d và 5.(4m+1) chia hết cho  d

20m + 4 chia hết cho d và 20m + 5 chia hết cho d

[ (20m + 5) - (20m + 4) ]  chia hết cho d

20m + 5 - 20m - 4 chia hết cho d

1 chia hết cho d 

⇒ d = 1

Vậy: 5m + 1 và 4m + 1 là cặp số nghuyên tố cùng nhau

\(A=5+5^2+....+5^{30}\)

\(A=\left(5+5^2+5^3\right)+\left(5^4+5^5+5^6\right)+...+\left(5^{28}+5^{29}+5^{30}\right)\)

\(A=5\cdot\left(1+5+25\right)+5^4\cdot\left(1+5+25\right)+...+5^{28}\cdot\left(1+5+25\right)\)

\(A=5\cdot31+5^4\cdot31+...+5^{28}\cdot31\)

\(A=31\cdot\left(5+5^4+...+5^{28}\right)\)

Vậy A chia hết cho 31

\(A=5+5^2+...+5^{30}\)

\(A=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{29}+5^{30}\right)\)

\(A=\left(5+25\right)+5\cdot\left(5+25\right)+...+5^{28}\cdot\left(5+25\right)\)

\(A=30+5\cdot30+...+5^{28}\cdot30\)

\(A=30\cdot\left(1+5+...+5^{28}\right)\)

Vậy A chia hết cho 30