\(x+2\cdot x+3\cdot x+...+100\cdot x=15150\)

\(\Rightarrow x\cdot\left(1+2+3+4+...+100\right)=15150\)

\(\Rightarrow x\cdot\left(100+1\right)\cdot\left[\left(100-1\right):1+1\right]:2=15150\)

\(\Rightarrow x\cdot101\cdot100:2=15150\)

\(\Rightarrow x\cdot5050=15150\)

\(\Rightarrow x=15150:5050\)

\(\Rightarrow x=3\)

Vậy: x=3

Mình ra x = 2 nha

\(\left(2x+1\right)^3=125\)

\(\Rightarrow\left(2x+1\right)^3=5^3\)

\(\Rightarrow2x+1=5\)

\(\Rightarrow2x=5-1\)

\(\Rightarrow2x=4\)

\(\Rightarrow x=\dfrac{4}{2}\)

\(\Rightarrow x=2\)

Vậy: x=2

( 2x + 1 ) mũ 3 = 125 

( 2x + 1 ) mũ 3 = 5 mũ 3

2x + 1 = 5

2x = 5 - 1

2x = 4

x = 4 : 2

x = 2

\(4^5:4^2-x=12\)

\(\Rightarrow4^{5-2}-x=12\)

\(\Rightarrow4^3-x=12\)

\(\Rightarrow64-x=12\)

\(\Rightarrow x=64-12\)

\(\Rightarrow x=52\)

Vậy: x=52

4^5 : 4^2 - x = 12

4^3 - x = 12

64 - x = 12

x = 64 - 12

x = 52

1) \(-4< x< 3\)

\(\Rightarrow x\in\left\{-3;-2;-1;0;1;2\right\}\)

Tổng:

\(\left(-3\right)+\left(-2\right)+\left(-1\right)+0+1+2\)

\(=\left(-2+2\right)+\left(-1+1\right)+0-3\)

\(=-3\)

2) \(-5< x< 5\)

\(\Rightarrow x\in\left\{-4;-3;-2;-1;0;1;2;3;4\right\}\)

Tổng:

\(\left(-4\right)+\left(-3\right)+\left(-2\right)+\left(-1\right)+0+1+2+3+3\)

\(=\left(-4+4\right)+\left(-3+3\right)+\left(-2+2\right)+\left(-1+1\right)+0\)

\(=0\)

3) \(-10< x< 6\)

\(\Rightarrow x\in\left\{-9;-8;-7;-6;-5;-4;-3;-2;-1;0;1;2;3;4;5\right\}\)

Tổng:

\(\left(-9\right)+\left(-8\right)+\left(-7\right)++\left(-6\right)+\left(-5\right)+\left(-4\right)+\left(-3\right)+\left(-2\right)+\left(-1\right)+0+1+2+3+4+5\)

\(=-24\)

4) \(-6< x< 5\)

\(\Rightarrow x\in\left\{-5;-4;-3;-2;-1;0;1;2;3;4\right\}\)

Tổng:

\(\left(-5\right)+\left(-4\right)+\left(-3\right)+\left(-2\right)+\left(-1\right)+0+1+2+3+4\)

\(=\left(-4+4\right)+\left(-3+3\right)+\left(-2+2\right)+\left(-1+1\right)+0-5\)

\(=-5\)

5) \(-5< x< 2\)

\(\Rightarrow x\in\left\{-4;-3;-2;-1;0;1\right\}\)

Tổng:

\(\left(-4\right)+\left(-3\right)+\left(-2\right)+\left(-1\right)+0+1\)

\(=\left(-1+1\right)+0+\left(-4-3-2\right)\)

\(=-6\)

\(\overline{abc}+\overline{bca}+\overline{cab}\)

\(=100a+10b+c+100b+10c+a+100c+10a+b\)

\(=111a+111b+111c\)

\(=111\left(a+b+c\right)⋮3\) (vì \(111⋮3\))

\(\Rightarrow\overline{abc}+\overline{bca}+\overline{cab}⋮3\left(dpcm\right)\)

\(x\inƯ\left(6\right)=\left\{1;2;3;6\right\}\)

\(x\in B\left(2\right)=\left\{2;4;6;8;10;.....\right\}\)

\(\left\{{}\begin{matrix}x\in U\left(6\right)=\left\{1;2;3;6\right\}\\x\in B\left(2\right)=\left\{2;4;6;8...\right\}\end{matrix}\right.\)

\(\Rightarrow x\in\left\{2;4;6\right\}\)

Gọi số cần tìm có dạng \(\overline{abc}\)

Chọn a từ tập \(\left\{1;2;3;...;9\right\}\): có 9 cách chọn

Chọn b từ tập \(\left\{0;1;2;3;...;9\right\}\): có 10 cách chọn

Chọn c từ tập \(\left\{0;5\right\}\): có 2 cách chọn.

Vậy ta có: \(9.10.2=180\left(tnđb\right)\)

Thoả mãn đề bài nhé

Lời giải:

$7^{a-2}=5^{2a-4}$

$\Rightarrow a-2=2a-4$

$\Rightarrow a-2=0$

$\Rightarrow a=2$

28 < x < 29

29< x < 35

vì a : 18 dư 9 nên a có dạng: a = 18k + 9 = 9.(2k + 1)

9⋮ 3 ⇒ a ⋮ 3; 

a = 18k + 9 = 6.(3k + 1) + 3 vì 6.(3k + 1) ⋮ 6 và 3 không chia hết cho 6 nên a không chia hết cho 6

gấp mn