b, \(\dfrac{x-3}{4}=\dfrac{15}{20}\)

<=> \(\dfrac{x-3}{4}=\dfrac{3}{4}\)

=> x-3=3

<=> x=6

Vậy x=6

\(a,\dfrac{x}{15}=\dfrac{4}{y}=\dfrac{-2}{5}\)

* \(\dfrac{x}{15}=\dfrac{-2}{5}\)

\(\Rightarrow\dfrac{x}{15}=\dfrac{-6}{15}\)

\(\Rightarrow x=-6\)

*\(\dfrac{4}{y}=\dfrac{-2}{5}\)

\(\Rightarrow\dfrac{4}{y}=\dfrac{4}{-10}\)

\(\Rightarrow y=-10\)

Vậy x = - 6 ; y = - 10

\(b,\dfrac{x-3}{4}=\dfrac{15}{20}\)

=> ( x - 3 ) . 20 = 4. 15

=> 20x - 60 = 60

=> 20x = 60 + 60

=> 20x = 120

=> x = 120 : 20

=> x = 6

Vậy x = 6

\(c,\dfrac{-5}{9}+\dfrac{-8}{15}+\dfrac{22}{-9}+\dfrac{-7}{15}< x\le\dfrac{-1}{3}+\dfrac{-1}{4}+\dfrac{-5}{12}\)

\(\Rightarrow\dfrac{-5}{9}+\dfrac{-8}{15}+\dfrac{-22}{9}+\dfrac{-7}{15}< x\le\dfrac{-4}{12}+\dfrac{-3}{12}+\dfrac{-5}{12}\)

\(\Rightarrow\left(\dfrac{-5}{9}+\dfrac{-22}{9}\right)+\left(\dfrac{-8}{15}+\dfrac{-7}{15}\right)< x\le-1\)

\(\Rightarrow-3+\left(-1\right)< x\le-1\)

\(\Rightarrow-4< x\le-1\)

\(\Rightarrow x=-3;-2;-1\)

a) 2^x.2^4=128

=>2^x.2^2=2^7

=>2^x=2^7:2^2

=>2^x=2^5

=>x=5

b)x^15=x

=>x^15-x=0

=>x(x^16-x)=0

=>2 trượng hợp:x=0 và x^16-1=0(x^16-1=0 cx 2 th nha)

b),d),e) như nhau nha!

c) dễ rồi

\(a)2^x\cdot4=128\)

\(\Rightarrow2^x=\frac{128}{4}\)

\(\Rightarrow2^x=32\)

\(\Rightarrow2^x=2^5\)

\(\Rightarrow x=5\)

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

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

\(\Rightarrow x(x^{14}-1)=0\)

\(\Rightarrow\hept{\begin{cases}x=0\\x^{14}-1=0\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x=0\\x^{14}=1\end{cases}\Rightarrow}\hept{\begin{cases}x=0\\x=1\end{cases}}\)

\(c)(2x+1)^3=125\)

\(\Rightarrow(2x+1)^3=5^3\)

\(\Rightarrow2x+1=5\)

\(\Rightarrow2x=5-1\)

\(\Rightarrow2x=4\)

\(\Rightarrow x=4:2=2\)

\(d)(x-5)^4=(x-5)^6\)

\(\Rightarrow(x-5)^6-(x-5)^4=0\)

\(\Rightarrow(x-5)^4\cdot\left[(x-5)^2-1\right]=0\)

\(\Rightarrow\orbr{\begin{cases}(x-5)^4=0\\(x-5)^2-1=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=0\\x=6\end{cases}}\)

\(e)(2x-15)^5=(2x-15)^3\)

\(\Rightarrow(2x-15)^5-(2x-15)^3=0\)

\(\Rightarrow(2x-15)^3-\left[(2x-15)^2-1\right]=0\)

\(\Rightarrow\orbr{\begin{cases}(2x-15)^3=0\\(2x-15)^2-1=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=\varnothing\\x=8\end{cases}}\)

Chúc bạn hoc tốt :>

Hack nao

A.(x+2)^x-1=15⁰

=>A.(x+2)^x-1=1

=> x + 2 = 1 hoặc x + 2 = -1 hoặc x - 1 = 0

=> x = -1 hoặc x = -3 hoặc x = 1.

B. (5-x)^x=1(x<5)

=> 5 - x = 1 hoặc 5 - x = -1 hoặc x = 0

=> x = 4 hoặc x = 6 hoặc x = 0.

C.15^x-2=225

=> 15^x-2=15²

=> x - 2 = 2 => x = 4.

D.(x+2)².(x+1)=64

=>(x+2).(x+2).(x+1)=64 = 1.2.32 = 2.2.16 = ...

Mà x + 2 và x + 2 và x + 1 chỉ hơn kém nhau 1 đơn vị nên không có x nào thỏa mãn.

E.(x-5)³.(x-5)=16

=>(x-5)⁴=16=2⁴

=>x-5=2=>x=7.

a, x¹⁰ = x²

=> x¹⁰ - x² = 0

=> x² (x⁸ - 1) = 0

=>x² = 0 hoặc x⁸ - 1 = 0

=>x = 0 hoặc x⁸ = 1

=>x=0 hoặc x=1

b, x+3/5 = 20/x+3

=> x+3 . x+3 = 5.20

=> (x+3)² = 100

=> (x+3)² = 10²

=> x+3 = 10

=> x = 7

c, làm tương tự giống phần a,

\(c,\left(2x-15\right)^2=\left(2x-15\right)^3\)

=> \(\left(2x-15\right)^2-\left(2x-15\right)^3=0\)

=> \(\left(2x-15\right)^2.\left[1-\left(2x-15\right)\right]=0\)

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

=> \(\left[{}\begin{matrix}2x-15=\sqrt{0}=0\\2x-15=1-0=1\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}2x=0+15=15\\2x=1+15=16\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}x=15:2=\frac{15}{2}\\x=16:2=8\end{matrix}\right.\)

Vậy \(x\in\left\{\frac{15}{2};8\right\}\)

Ta có 5\(\dfrac{1}{5}\)=5\(\dfrac{3}{15}\)

Từ đó ta tìm đc các phần nguyên của x là :5;6;7;8

\(\frac{15}{41}+\frac{-138}{41}< x< \frac{1}{2}+\frac{1}{3}+\frac{1}{6}\)

\(\Leftrightarrow\frac{-123}{41}< x< \frac{1.3+1.2+1}{6}\)

\(\Leftrightarrow-3< x< 1\)

\(\Rightarrow x\in\left\{-2;-1;0\right\}\)

\(\frac{x}{5}=\frac{15}{2}-\frac{51}{10}\)

\(\frac{x}{5}=\frac{15.5-51}{10}\)

\(\frac{x}{5}=\frac{24}{10}\)

\(\frac{x}{5}=\frac{12}{5}\)

\(x=12\)

Ta có : (3¹⁵ x 4 + 3¹⁵ x 5) : 3¹⁶

= 3¹⁵.(4 + 5) : 3¹⁶

= 3¹⁵.9 : 3¹⁶

= 3¹⁵.3² : 3¹⁶

= 3¹⁷ : 3¹⁶

= 3

=3¹⁵ x (4+5) :3¹⁶

=3¹⁵ x9 : 3¹⁶

=3¹⁵x3²:3¹⁶

=3¹⁵⁺²:3¹⁶

=3¹⁷:3¹⁶

=3¹

=3

=-27/5x -4/15 + -4/15x2010 - -4/15x-27/5                                                                                                                                                            =-4/15x2010                                                                                                                                                                                                         =-52