1. Tìm x, biết:

a) \(\frac{4}{x}=\frac{8}{6}\). Ta có: \(\frac{8}{6}=\frac{8:2}{6:2}=\frac{4}{3}\Rightarrow x=3\)

b) \(\frac{3}{x-5}=\frac{4}{x+2}\). Ta có: \(5-2=3\)

\(\Rightarrow x=\left(3.5\right)+\left(4.2\right)+3=15+8+3=26\)

c) \(\frac{x}{-2}=\frac{-8}{x}\Rightarrow x=\left(-8\right):\left(-2\right)=4\)

2. Rút gọn

a) \(\frac{2^4.5^2.11^2.7}{2^3.5^3.7^2.11}\Leftrightarrow\frac{2^3.2^1.5^2.11.11.7}{2^3.5^2.5^1.7.7.11}\Leftrightarrow\frac{2^1.11}{5^1.7}=\frac{22}{35}\)

b) Tương tự

c) Tương tự

\(\frac{4}{x}=\frac{8}{6}\Rightarrow x=\frac{4.6}{8}=3\)

\(\frac{3}{x-5}=\frac{-4}{x+2}\Rightarrow3\left(x+2\right)=-4\left(x-5\right)\)

                                \(\Rightarrow3x+6=-4x+20\)

                                \(\Rightarrow3x+4x=20-6\)

                                \(\Rightarrow7x=14\)

                                \(\Rightarrow x=2\)

\(\frac{x}{-2}=\frac{-8}{x}\Rightarrow x^2=\left(-8\right)\left(-2\right)=16\Rightarrow x=\pm4\)

\(\frac{4}{x}=\frac{8}{6}\)

\(\Rightarrow4\cdot6=x\cdot8\)

\(\Rightarrow x=\frac{4\cdot6}{8}\)

\(\Rightarrow x=3\)

a) (2x - 3)² = 16

=> (2x - 3)² = 4²

=> \(\orbr{\begin{cases}2x-3=4\\2x-3=-4\end{cases}}\)

=> \(\orbr{\begin{cases}2x=7\\2x=-1\end{cases}}\)

=> \(\orbr{\begin{cases}x=\frac{7}{2}\\x=-\frac{1}{2}\end{cases}}\)

Vậy ...

b) 2.3^{x + 2} + 4. 3^{x + 1} = 10.3⁶

=> 2.3^{x + 1}. 3 + 4.3^{x + 1} = 10 . 3⁶

=> 6.3^{x + 1} + 4.3^{x + 1} = 10.3⁶

=> (6 + 4).3^{x + 1}= 10.3⁶

=> 10.3^{x + 1}= 10.3⁶

=> 3^{x + 1}= 3⁶

=> x + 1 = 6

=> x = 6 - 1

=> x = 5

\(a,\left(2x-3\right)^2=16\)

\(\Rightarrow\left(2x-3\right)^2=4^2\)

\(\Rightarrow2x-3=4\)

\(2x=4+3\)

\(2x=7\)

\(x=7:2\)

\(x=\frac{7}{2}\)

Tìm x 
a.(2x - 3)² =16

 => 2x - 3 = \(\pm4\)                           

2x-3 = 4                                                        2x - 3 = -4

=> x = \(\frac{3}{2}\)                                                            => x =  \(-\frac{1}{2}\)

Số số hạng là :

      (2x - 2) : 2 + 1 = x - 1 + 1 = x (số)

Tổng là : 

       (2x + 2).x : 2 = 210

=> (2x² + 2x) : 2 = 210

=> x² + x = 210

=> x(x + 1) = 210

=> x(x + 1) = 20.21

=> x = 20

Vậy x = 20 

Ta có : \(\frac{x}{2}=\frac{10}{x+1}\)

=> x(x + 1) = 10.2

=> x(x + 1) = 20

=> sai đề 

a)2^x+1.3^y=12^x

2^x+1.3^y=(3.4)^x=3^x.2^2x

3^y-x=2^x-1

y-x=x-1=0

x=y=1

a) (4x - 1)² = 25.9

=> (4x - 1)² = 5² . 3² = 15²

=> 4x - 1 = 15

=> 4x = 16

=> x = 4

b) 2^x + 2^x+3 = 144

=> 2^x + 2^x . 2³ = 144

=> 2^x (1 + 2³) = 144

=> 2^x . 9 = 144

=> 2^x = 16

=> x = 4

c) đề chắc chắn đúng chứ :v

d) (2x + 1)³ - 12 = 15

=> (2x + 1)³ = 27

=> (2x + 1)³ = 3³

=> 2x + 1 = 3 => 2x = 2 => x = 1

2. 2^x = 16 => 2^x = 2⁴ => x = 4

3^x = 81 => 3^x = 3⁴ => x = 4

x³ = 64 => x³ = 4³ => x = 4

x² =81 => x² = 9² => x = 9

Câu c sai đề đó ạ

c) 2.3^x = 10.3¹² + 8.27⁴

2\(^x\)- 15 = 17

\(\Rightarrow\)2\(^x\) =  32

\(\Rightarrow\)x  = 5

2^x-15=17

=>2^x=17+15

=2^x=32

=>2^x=2^5

=>x=5