\(2^{x+1}\cdot2^{2014}=2^{2015}\\ 2^{x+1}=2^{2015}:2^{2014}\\ 2^{x+1}=2\\ =>x+1=1\\ x=1-1\\ x=0\)

a) 89-(73-x) = 20

=> 73+x =89-20

=> 73+x=69

=> x=69-73

=> x=-4

b) (x+7)-25=13

=> x+7=13+25

=> x+7=38

=> x=38-7

=> x=31

c) 98-(x+4)=20

=> x+4=98-20

=> x+4=78

=> x=78-4

=> x=73

d) 140:(x-8)=7

=> x-8=140:7

=> x-8=20

=> x=20+8

=> x=28

e) 4(x+41)=400

=> x+41=400:4

=> x+41=100

=> x=100-41

=> x=59

f) x-[42+(-28)]=-8

=> x-14=-8

=> x=-8+14

=> x=6

g) x+5=20-(12-7)

=> x+5=20-5

=> x+5=15

=> x=15-5

=> x=10

h) \(x-11=2.2^3+20:5\)

=> x-11=2.8+4

=> x-11=16+4

=> x-11=20

=> x=20+11

=> x=31

i) \(4\left(x-3\right)=7^2-1^3\)

=> 4(x-3)=49-1

=> 4(x-3)=48

=> x-3=48:4

=> x-3=12

=> x=12+3

=> x=15

a) \(5x-65=5.3^2 \\ 5x-65=45\\5x=45+65\\5x=110\\x=22\)

b) \(200-(2x+6)=4^3\\2x+6=200-4^3\\2x+6=136\\2x=130\\x=65\)

c) \(2(x-51)=2.2^3+20\\2(x-51)=16+20\\2(x-51)=36\\x-51=18\\x=51+18=69\)

d) \(135-5(x+4)=35\\5(x+4)=135-45\\5(x-4)=90\\x-4=18\\x=18+4=22\)

e) \((2x-4)(15-3x)=0\\2(x-2).3(5-x)=0\\(x-2)(5-x)=0\\ \left[ \begin{array}{l}x-2=0\\5-x=0\end{array} \right. \\ \left[ \begin{array}{l}x=2\\x=5\end{array} \right.\)

f) \(2^{x+1} . 2^{2014}=2^{2016} \\ (2^{x+1} . 2^{2014}):2^{2014}=2^{2016} :2^{2014} \\ 2^{x=1}=2^{2016-2014} \\2^{x+1}=2^2\\x+1=2\\x=1\)

g) \(15+(x-1)^3=43\\(x-1)^3=15-42\\(x-1)^3=-27\\(x-1)^3=(-3)^3\\x-1=-3\\x=-2\)

h) \(15-x=17+(-9)\\15-x=17-9\\15-x=8\\x=15-8\\x=7\)

i) \(|x-5|=|-7|+|-4|\\|x-5|=7+4\\|x-5|=11\\ \left[ \begin{array}{l}x-5=11\\x-5=-11\end{array} \right. \\ \left[ \begin{array}{l}x=16\\x=-6\end{array} \right.\)

k) \(|x-3|-12=-9+|-7|\\|x-3|-12=-9+7\\|x-3|-12=-2\\|x-3|=10 \\ \left[ \begin{array}{l}x-3=10\\x-3=-10\end{array} \right. \\ \left[ \begin{array}{l}x=13\\x=-7\end{array} \right.\)

c)  2 2016 . 2 x - 1 = 2 2015

2 x - 1 = 2 2015 : 2 2016

2 x - 1 = 2 2015 - 2016

2 x - 1 = 2 - 1

⇒ x – 1 = -1

x = -1 + 1

x = 0

\(A=1+2^1+2^2+...+2^{2015}\)

\(2\cdot A=2^1+2^2+2^3+...+2^{2015}+2^{2016}\)

\(2A-A=2^1+2^2+2^3+...+2^{2015}+2^{2016}-\left(1+2^1+2^2+...+2^{2015}\right)\)

\(A=2^{2016}-1\)

\(B=2^{2018}-2^{2017}-2^{2016}-2^{2015}-2^{2014}\)

\(=>2B=2^{2019}-2^{2018}-2^{2017}-2^{2016}-2^{2015}\)

\(=>2B+B=2^{2019}-2^{2014}\)

\(=>B=\dfrac{2^{2019}-2^{2014}}{3}\)

A= 22015*72020

=1585520300

`#3107`

\(A=1+2^1+2^2+2^3+...+2^{2015}\)

\(2A=2+2^2+2^3+2^4+...+2^{2016}\)

\(2A-A=\left(2+2^2+2^3+2^4+...+2^{2016}\right)-\left(1+2+2^2+2^3+...+2^{2015}\right)\)

\(A=2+2^2+2^3+2^4+...+2^{2016}-1-2-2^2-2^3-...-2^{2015}\)

\(A=2^{2016}-1\)

Vậy, \(A=2^{2016}-1.\)

\(A=2^0+2^1+2^2+...+2^{2015}\)

\(2\cdot A=2^1+2^2+2^3+...+2^{2016}\)

\(A=2A-A=2^{2016}-2^0\)

\(A=2^{2016}-1\)