\(5n⋮2\Rightarrow n⋮2\)

\(\Rightarrow n=\left\{2;-2\right\}\)

Mọi số tự nhiên $n$ chẵn đều thỏa mãn đề bài.

a) \(\left(x-1\right)^3=8=2^3\)

\(x-1=2\)

\(x=2+1=3\)

b) \(7^{2x-6}=49=7^2\)

\(2x-6=2\)

\(2x=6+2=8\)

\(x=8:2=4\)

c) \(\left(2x-14\right)^7=128=2^7\)

\(2x-14=2\)

\(2x=14+2=16\)

\(x=16:2=8\)

d) \(x^4\cdot x^5=5^3\cdot5^6=5^4\cdot5^5\)

\(x=5\)

e) \(3\cdot\left(x+2\right):7\cdot4=120\)

\(x+2=120:3\cdot7:4\)

\(x+2=70\)

\(x=70-2=68\)

Lời giải:

a. $(x-1)^3=8=2^3$
$\Rightarrow x-1=2$

$\Rightarrow x=3$

b. $7^{2x-6}=49=7^2$
$\Rightarrow 2x-6=2$

$\Rightarrow 2x=8$

$\Rightarrow x=4$

c. $(2x-14)^7=128=2^7$

$\Rightarrow 2x-14=2$

$\Rightarrow 2x=16$

$\Rightarrow x=18$

d.

$x^4.x^5=5^3.5^6$

$x^9=5^9$

$\Rightarrow x=5$

e. 

$3(x+2):7=120:4=30$

$3(x+2)=30.7=210$

$x+2=210:3=70$

$x=70-2=68$

\(B\left(5\right)=\left\{0;5;10;15;20;...\right\}\)

\(B\left(-5\right)=\left\{0;-5;-10;-15;-20;...\right\}\)

=\(\dfrac{-133}{9}\)

\(1024\div2^5+140\div\left(38+5^2\right)-7^{23}\div7^{21}\)

\(=1024\div32+140\div\left(38+25\right)-7^{23}\div7^{21}\)

\(=32+140\div63-7^2\)

\(=32+\dfrac{20}{9}-49\)

\(=\dfrac{308}{9}-49\)

\(=-\dfrac{133}{9}\)

khó dị 

`( x+2 ) +(x+5)+(x+8)+...+(x+59)=670`

`=> (x+x+x+...+x) +(2+5+8+...+59)=670`

Số số hạng là :

`(59-2) : 3+1=1=20`

Tổng dãy là :

`(59+2) * 20 : 2=610`

`20x+610=670`

`=> 20x=670-610`

`=>20x= 60`

`=>x=60:20`

`=>x=3`

\(\left(x+\dfrac{1}{2}\right)^2=\dfrac{4}{9}\\ \Leftrightarrow\left(x+\dfrac{1}{2}\right)^2=\left(\dfrac{2}{3}\right)^2\\ \Leftrightarrow\left[{}\begin{matrix}x+\dfrac{1}{2}=\dfrac{2}{3}\\x+\dfrac{1}{2}=-\dfrac{2}{3}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{6}\\x=-\dfrac{7}{6}\end{matrix}\right.\)

Vậy...

\(\left(x+\dfrac{1}{2}\right)^2=\dfrac{4}{9}\)

\(\left(x+\dfrac{1}{2}\right)^2=\left(\dfrac{2}{3}\right)^2\)

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

\(x=\dfrac{2}{3}-\dfrac{1}{2}=\dfrac{4}{6}-\dfrac{3}{6}\)

\(=\dfrac{1}{6}\)