a) \(\left(x-6\right)^3=\left(x-6\right)^2\Leftrightarrow\orbr{\begin{cases}x-6=1\Leftrightarrow x=7\\x-6=0\Leftrightarrow x=6\end{cases}}\)

b) \(\left(7.x-11\right)^3=2^5.5^2+200\)

\(\Leftrightarrow\left(7.x-11\right)^3=800+200\)

\(\Leftrightarrow\left(7.x-11\right)^3=1000\)

\(\Leftrightarrow\left(7.x-11\right)^3=10^3\)

\(\Leftrightarrow7x-11=10\Leftrightarrow7x=21\Leftrightarrow x=3\)

c) \(3+2^{x-1}=24-\left[4^2-\left(2^2-1\right)\right]\)

\(\Leftrightarrow3+2^{x-1}=24-\left[4^2-3\right]\)

\(\Leftrightarrow3+2^{x-1}=24-13\)

\(\Leftrightarrow3+2^{x-1}=11\)

\(\Leftrightarrow2^{x-1}=8\Leftrightarrow2^{x-1}=2^3\Leftrightarrow x-1=3\Leftrightarrow x=4\)

a)\(3^x.3=243\Leftrightarrow3^x=81\Leftrightarrow3^x=3^4\Leftrightarrow x=4\)

b) \(2^x.16^2=1024\Leftrightarrow2^x.256=1024\Leftrightarrow2^x=4\Leftrightarrow2^x=2^2\Leftrightarrow x=2\)

c) \(64:4^x=16^8\Leftrightarrow4^x=67108864\Leftrightarrow4^x=4^{13}\Leftrightarrow x=13\)

d) \(2^x=16\Leftrightarrow2^x=2^4\Leftrightarrow x=4\)

\(2^{10}.2^{x+4}=64^5\)

\(\Leftrightarrow2^{x+14}=2^{30}\)

\(\Leftrightarrow x+14=30\)

\(\Leftrightarrow x=16\)

\(5^x+5^{x+3}=630\)

\(\Rightarrow5^x.1+5^x.125=630\)

\(\Rightarrow5^x.126=630\)

\(\Rightarrow5^x=5\)

\(\Rightarrow x=1\)

\(x+\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+..............+\left(x+100\right)=7450\)

\(\Rightarrow\left(x+x+x+x+.........+x\right)+\left(1+2+3+..........+100\right)=7450\)

\(101x+5050=7450\)

Đến đây tự tính

Bài 1 : 

a) (x-15 ) .32 = 32 

<=> (x - 15 )  = 1 

<=>  x           = 1 + 15 

<=> x           = 16

Vậy x = 90

b) ( x- 15 ) - 75 = 0

<=> x- 15          = 75 

<=> x                = 75 + 15 

<=>  x                 = 90 

Vậy x= 90

c) 315 +(125 - x ) =435

<=> 125 -x            = 435 - 315 

<=> 125  - x          = 120 

<=> x                     = 125 - 120 

<=>  x                    = 5 

Vậy x = 5 

d) (x-78 ) . 2020 = 0

<=> x- 78           = 0 

<=>  x                 = 0 + 78 

<=>  x                  = 78 

Vậy x = 78 

e) 219 - 7. ( x + 1 )= 0 

<=> 7.(x + 1 )         = 219 

<=> 7x + 7             = 219

<=>   7x                 = 212

<=>  x                    = 212 /7 ( L ) 

Vậy x \(\in\varnothing\)

g) 3^x .3 = 243

<=> 3 ^x   = 81

<=> 3^x      = 3⁴

<=>   x       = 4

Vậy x = 4 

Phần h) bạn làm tương tự 

Bài 2 : 

Mình đang làm ,lát mình làm xong rồi gửi,tầm 4:30 h gì đó ,vì mình đang học trực tuyến !

bài 2 : 

a) Ta có : 2¹⁶¹ > 2¹⁶⁰ = (2⁴ )⁴⁰ =16⁴⁰     > 13⁴⁰ 

Vậy 13⁴⁰ < 2¹⁶¹

b) 1024⁹ = (2¹⁰)⁹ = 2 ⁹⁰ 

2¹⁰⁰ = 2¹⁰⁰ 

=> ta thấy 2⁹⁰ < 2¹⁰⁰  => 1024⁹ < 2¹⁰⁰ 

c) tương tự d) nha bạn ,thực ra mình làm d) trước

d) 48 . ( 4 + 8 ) = 48 . 12 = 576 

4³ + 8³ = 576 

=> 48.(4 + 8 ) = 4³ + 8³ 

a.3     d.12

b.1     e.5

c.6    g. 2

\(a,x^3=27\)

\(\Rightarrow x^3=3^3\)

\(\Rightarrow x=3\)

\(b,\left(2x-1\right)^3=8\)

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

\(\Rightarrow2x-1=2\)

\(\Rightarrow2x=3\)

\(\Rightarrow x=\frac{3}{2}\)

\(c,\left(x-2\right)^2=16\)

\(\Rightarrow\left(x-2\right)^2=4^2\)

\(\Rightarrow x-2=4\)

\(\Rightarrow x=6\)

\(d,\left(x-5\right)^2=49\)

\(\Rightarrow\left(x-5\right)^2=7^2\)

\(\Rightarrow x-5=7\)

\(\Rightarrow x=12\)

\(e,\left(2x-1\right)^2=81\)

\(\Rightarrow\left(2x-1\right)^2=9^2\)

\(\Rightarrow2x-1=9\)

\(\Rightarrow2x=10\)

\(\Rightarrow x=5\)

\(g,\left(4x-3\right)^3=125\)

\(\Rightarrow\left(4x-3\right)^3=5^3\)

\(\Rightarrow4x-3=5\)

\(\Rightarrow4x=8\)

\(\Rightarrow x=2\)

B1:

Ta có: \(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\frac{2^{12}.3^{10}-2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)

\(=\frac{2^{12}.3^{10}-2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^{12}.3^{10}.\left(1-5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}\)

\(=\frac{2.\left(-4\right)}{3.5}=-\frac{8}{15}\)

B2:

Ta có: \(1+3+5+...+x=1600\)

\(\Leftrightarrow\frac{\left(x+1\right)\cdot\left(\frac{x-1}{2}+1\right)}{2}=1600\)

\(\Leftrightarrow\left(x+1\right)\cdot\frac{x+1}{2}=3200\)

\(\Leftrightarrow\left(x+1\right)^2=6400\)

Xét theo dãy tăng tiến ta thấy được giá trị của x càng tăng

=> x dương => x + 1 dương

\(\Rightarrow x+1=80\)

\(\Rightarrow x=79\)

3^(x + 1) - 3^x = 54

3^x(3 - 1) = 54

3^x.2 = 54

3^x = 54: 2

3^x = 27

3^x = 3^3

x =3

Vậy x = 3

Câu 1:

12\(^{a}\) : 2\(^{a-8}\) = 3\(^{b-9}\).2009\(^{20-c}\)

12\(^{a}\) = 2\(^{a-b}\).3\(^{b-9}\).2009\(^{20-c}\)

2\(^{2a}\).3\(^{a}\).2009\(^0\) = 2\(^{a-b}\).3\(^{b-9}\).2009\(^{20-c}\)

\(\begin{cases}2a=a-8\\ b-9=a\\ 20-c=0\end{cases}\)

\(\begin{cases}2a-a=8\\ b=a+9\\ c=20\end{cases}\)

\(\begin{cases}a=8\\ b=9+8\\ c=20\end{cases}\)

\(\begin{cases}a=8\\ b=9\\ c=20\end{cases}\)

(a; b; c) = (8; 9; 20)

3^(x + 1) - 3^x = 54

3^x(3 - 1) = 54

3^x.2 = 54

3^x = 54: 2

3^x = 27

3^x = 3^3

x =3

Vậy x = 3

Câu 1:

12\(^{a}\) : 2\(^{a-8}\) = 3\(^{b-9}\).2009\(^{20-c}\)

12\(^{a}\) = 2\(^{a-b}\).3\(^{b-9}\).2009\(^{20-c}\)

2\(^{2a}\).3\(^{a}\).2009\(^0\) = 2\(^{a-b}\).3\(^{b-9}\).2009\(^{20-c}\)

\(\begin{cases}2a=a-8\\ b-9=a\\ 20-c=0\end{cases}\)

\(\begin{cases}2a-a=8\\ b=a+9\\ c=20\end{cases}\)

\(\begin{cases}a=8\\ b=9+8\\ c=20\end{cases}\)

\(\begin{cases}a=8\\ b=9\\ c=20\end{cases}\)

(a; b; c) = (8; 9; 20)

Tìm x,biết :

câu 1: (x+8)^2=7225

(x + 8)^2 = 85^2

x + 8 = -85 hoặc x + 8 = 85

x + 8 = - 85

x = - 85 - 8

x = - 93

x + 8 = 85

x = 85 - 8

x = 77

Vậy x ∈ {-93; 77}

Câu 2: x^2-190=710

x^2 = 710 + 190

x^2 = 900

x^2 = 30^2

x = -30 hoặc x = 30

Vậy x ∈ {-30; 30}

4^x= 2^x+1

4^x= 2^x. 2¹

4^x:2^x= 2

2^x=2¹

=> x=1

Vậy...