`#3107.101107`

a,

$2014^{15} . (2x - 60) = 2014^{16}$

$\Rightarrow 2x - 60 = 2014^{16} \div 2014^{15}$

$\Rightarrow 2x - 60 = 2014$

$\Rightarrow 2x = 2074$

$\Rightarrow x = 1037$

Vậy, `x = 1037`

b,

`x + 18 \div 3^2 = 5.4^2`

`\Rightarrow x + 18 \div 9 = 5.16`

`\Rightarrow x + 9 = 80`

`\Rightarrow x = 80 - 9`

`\Rightarrow x = 71`

Vậy, `x = 71`

c,

`7.(42 - x) = 5^3 + 134`

`\Rightarrow 7.(42 - x) = 125 + 134`

`\Rightarrow 7(42 - x) = 259`

`\Rightarrow 42 - x = 259 \div 7`

`\Rightarrow 42 - x = 37`

`\Rightarrow x = 42 - 37`

`\Rightarrow x = 5`

Vậy, `x = 5.`

a: 3x+21=57

=>3x=57-21

=>3x=36

=>\(x=\dfrac{36}{3}=12\)

b: \(2x-138=2^3\cdot3^2\)

=>\(2x-138=8\cdot9=72\)

=>2x=72+138=210

=>x=105

c: \(4x^3+12=120\)

=>\(4x^3=120-12=108\)

=>\(x^3=27=3^3\)

=>x=3

\(a)3x+21=57\\ \Leftrightarrow3x=57-21\\ \Leftrightarrow3x=36\\ \Leftrightarrow x=\dfrac{36}{3}\\ \Leftrightarrow x=12\\ b)2x-138=2^3\cdot3^2\\ \Leftrightarrow2x-138=72\\ \Leftrightarrow2x=72+138\\ \Leftrightarrow2x=210\\ \Leftrightarrow x=\dfrac{210}{2}\\ \Leftrightarrow x=105\\ c)4x^3+12=120\\ \Leftrightarrow4x^3=120-12\\ \Leftrightarrow4x^3=108\\ \Leftrightarrow x^3=\dfrac{108}{4}\\ \Leftrightarrow x^3=27\\ \Leftrightarrow x^3=3^3\\ \Leftrightarrow x=3.\)

\(\left(2x-1\right)^5=x^5\)

\(2x-1=x\)

\(2x-x=1\)

\(x=1\)

_________________________

\(2x^2+2=20\)

\(2x^2=20-2\)

\(2x^2=18\)

\(x^2=\dfrac{18}{2}\)

\(x^2=9\)

\(x=\pm3\)

Xét tổng : 1+3+...+149+151

Số số hạng dãy trên :

  (151-1):2+1=76(số)

Tổng dãy trên :

   (151+1)x76:2=5738

Lại có : (-1)+(-3)+...+(-149)+(-151)

= -(1+3+...+149+151)

= -5738

ta có, dãy số trên có số số hạng là:

(151 - 1) : 2 + 1 = 76 (số hạng)

tổng các dãy số trên là: (vì là phép cộng của các số âm nên ta bỏ dấu âm rồi tính như bình thường, kết quả nhận lại thêm vào dấu âm.)

(151 + 1) x 76 : 2 = 5776

=> (-1) + (-3) +....+ (-149) + (-151) = (-5776)

`@` `\text {Ans}`

`\downarrow`

`a)`

\(5^x+5^{x+2}=650\)

`\Rightarrow 5^x + 5^x . 5^2 = 650`

`\Rightarrow 5^x . (1 + 5^2) = 650`

`\Rightarrow 5^x . 26 = 650`

`\Rightarrow 5^x = 650 \div 26`

`\Rightarrow 5^x = 25`

`\Rightarrow 5^x = 5^2`

`\Rightarrow x = 2`

Vậy, `x = 2`

`b)`

`(4x + 1)^2 = 25.9`

`\Rightarrow (4x + 1)^2 = 225`

`\Rightarrow (4x + 1)^2 = (+-15^2)`

`\Rightarrow`\(\left[{}\begin{matrix}4x-1=15\\4x-1=-15\end{matrix}\right.\)

`\Rightarrow `\(\left[{}\begin{matrix}4x=16\\4x=-14\end{matrix}\right.\)

`\Rightarrow `\(\left[{}\begin{matrix}x=4\\x=-\dfrac{7}{2}\end{matrix}\right.\)

Vậy, `x \in`\(\left\{-\dfrac{7}{2};4\right\}\)

`c)`

\(2^x+2^{x+3}=144\)

`\Rightarrow 2^x + 2^x . 2^3 = 144`

`\Rightarrow 2^x . (1 + 2^3) = 144`

`\Rightarrow 2^x . 9 = 144`

`\Rightarrow 2^x = 144 \div 9`

`\Rightarrow 2^x = 16`

`\Rightarrow 2^x = 2^4`

`\Rightarrow x = 4`

Vậy, `x = 4`

`d)`

\(3^{2x+2}=9^{x+3}\)

`\Rightarrow `\(3^{2x+2}=\left(3^2\right)^{x+3}\)

`\Rightarrow `\(3^{2x+2}=3^{2x+6}\)

`\Rightarrow 2x + 2 = 2x + 6`

`\Rightarrow 2x - 2x = 6 - 2`

`\Rightarrow 0 = 4 (\text {vô lý})`

Vậy, `x` không có giá trị nào thỏa mãn.

`e)`

\(x^{15}=x^2\)

`\Rightarrow `\(x^{15}-x^2=0\)

`\Rightarrow `\(x^2\cdot\left(x^{13}-1\right)=0\)

`\Rightarrow `\(\left[{}\begin{matrix}x^2=0\\x^{13}-1=0\end{matrix}\right.\)

`\Rightarrow `\(\left[{}\begin{matrix}x=0\\x^{13}=1\end{matrix}\right.\)

`\Rightarrow `\(\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

Vậy, `x \in`\(\left\{0;1\right\}.\)

\(a,5^x+5^{x+2}=650\\ \Rightarrow5^x+5^x.5^2=650\\ \Rightarrow5^x\left(1+5^2\right)=650\\ \Rightarrow5^x.26=650\\ \Rightarrow5^x=25\\ \Rightarrow5^x=5^2\\ \Rightarrow x=2\)

\(b,\left(4x+1\right)^2=25.9\\\Rightarrow\left(4x+1\right)^2=225\\ \Rightarrow\left[{}\begin{matrix}4x+1=15\\4x+1=-15\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{7}{2}\\x=-4\end{matrix}\right.\)

\(c,2^x+2^{x+3}=144\\ \Rightarrow2^x+2^x.2^3=144\\ \Rightarrow2^x\left(1+2^3\right)=144\\ \Rightarrow2^x=144:\left(1+2^3\right)\\ \Rightarrow2^x=16\\ \Rightarrow2^x=2^4\\ \Rightarrow x=4\)

\(d,3^{x+2}=9^{x+3}\\ \Rightarrow3^{x+2}=\left(3^2\right)^{x+3}\\ \Rightarrow3^{x+2}=3^{2x+6}\\ \Rightarrow x+2=2x+6\\ \Rightarrow x-2x=6-2\\ \Rightarrow-x=4\\ \Rightarrow x=-4\)

\(e,x^{15}=x^2\\ \Rightarrow x^{15}-x^2=0\\ \Rightarrow x^2\left(x^{13}-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x^2=0\\x^{13}-1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

a: =>5^x+5^x*25=650

=>5^x*26=650

=>5^x=25

=>x=2

b: =>4x+1=15 hoặc 4x+1=-15

=>4x=-16 hoặc 4x=14

=>x=7/2 hoặc x=-8

c: =>2^x*9=144

=>2^x=16

=>x=4

d: =>2x+2=2x+6

=>2=6(loại)

e: =>x^2(x^13-1)=0

=>x=0 hoặc x=1

\(f,\left(2x+1\right)^3=343\\\Rightarrow \left(2x+1\right)^3=7^3\\ \Rightarrow2x+1=7\\ \Rightarrow2x=6\\ \Rightarrow x=3\\ g,\left(x-1\right)^3=125\\ \Rightarrow\left(x-1\right)^3=5^3\\ \Rightarrow x-1=5\\ \Rightarrow x=6\\ h,2^{x+2}-2^x=96\\ \Rightarrow2^x.2^2-2^x=96\\ \Rightarrow2^x.\left(2^2-1\right)=96\\ \Rightarrow2^x=96:\left(2^2-1\right)\\ \Rightarrow2^x=32\\ \Rightarrow2^x=2^5\\ \Rightarrow x=5\)

\(i,\left(x-5\right)^4=\left(x-5\right)^6\\ \Rightarrow\left(x-5\right)^4\left(1-\left(x-5\right)^2\right)=0\\\Rightarrow\left[{}\begin{matrix}\left(x-5\right)^4=0\\1-\left(x-5\right)^2=0\end{matrix}\right. \\ \Rightarrow\left[{}\begin{matrix}x-5=0\\x-5=1\\x-5=-1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\left(t/m\right)\\x=6\left(t|m\right)\\x=4\left(loại\right)\end{matrix}\right.\)

\(j,720:\left[41-\left(2x-5\right)\right]=2^3.5\\ \Rightarrow720:\left(41-2x+5\right)=40\\ \Rightarrow\left(46-2x\right)=720:40\\ \Rightarrow46-2x=18\\ \Rightarrow2x=46-18=28\\ \Rightarrow x=28:2=14\)

@seven

f: =>2x+1=7

=>2x=6

=>x=3

g: =>x-1=5

=>x=6

h: =>2^x*3=96

=>2^x=32

=>x=5

i: =>(x-5)^4*[(x-5)^2-1]=0

=>(x-5)(x-4)(x-6)=0

=>x=5;x=4;x=6

j: =>41-(2x-5)=720:40=18

=>2x-5=23

=>2x=28

=>x=14

f)

`(2x+1)^3=343`

`(2x+1)^3=7^3`

`=>2x+1=7`

`2x=7-1`

`2x=6`

`x=6:2`

`x=3`

g)

`(x-1)^3 =125`

`(x-1)^3 =5^3`

`=>x-1=5`

`x=6`

h)

`2^(x+2)-2^x=96`

`2^x *2^2 -2^x =96`

`2^x (2^2 -1)=96`

`2^x *3=96`

`2^x =32`

`2^x =2^5`

`=>x=5`

i)

`(x-5)^4 =(x-5)^6` (`x>=5`)

`(x-5)^6 -(x-5)^4 =0`

`(x-5)^4 [(x-5)^2 -1]=0`

`=>x-5=0` hoặc `(x-5)^2 -1=0`

`<=>x=5` hoặc `(x-5)^2 =1`

`<=>x=5` hoặc `x-5=1` hoặc `x-5=-1`

`<=>x=5` hoặc `x=6` hoặc `x=4`

j)

`720:[41-(2x-5)]=2^3 *5`

`720:[41-(2x-5)]=8*5`

`720:[41-(2x-5)]=40`

`41-(2x-5)=720:40`

`41-(2x-5)=18`

`2x-5=41-18`

`2x-5=23`

`2x=28`

`x=14`

xy=-11, x<y

x,y nguyên => \(\hept{\begin{cases}x=-11\\y=1\end{cases}}\)

Vậy (x;y)=(-11;1)

\(\dfrac{7}{1}:\dfrac{4}{1}=\dfrac{7}{1}.\dfrac{1}{4}=\dfrac{7}{4}\)

\(\dfrac{11}{7}:\dfrac{37}{9}=\dfrac{11}{7}.\dfrac{9}{37}=\dfrac{99}{259}\)

7/1 x 1/4 = 7/4

11/7 x 9/37 = 99/259