a) \(4^n=4096\Rightarrow4^n=4^6\Rightarrow n=6\)

b) \(5^n=15625\Rightarrow5^n=5^6\Rightarrow n=6\)

c) \(6^{n+3}=216\Rightarrow6^{n+3}=6^3\Rightarrow n+3=3\Rightarrow n=0\)

d) \(x^2=x^3\Rightarrow x^3-x^2=0\Rightarrow x^2\left(x-1\right)=0\Rightarrow\left[{}\begin{matrix}x=0\\x-1=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

e) \(3^{x-1}=27\Rightarrow3^{x-1}=3^3\Rightarrow x-1=3\Rightarrow x=4\)

f) \(3^{x+1}=9\Rightarrow3^{x+1}=3^2\Rightarrow x+1=2\Rightarrow x=1\)

g) \(6^{x+1}=36\Rightarrow6^{x+1}=6^2\Rightarrow x+1=2\Rightarrow x=1\)

h) \(3^{2x+1}=27\Rightarrow3^{2x+1}=3^3\Rightarrow2x+1=3\Rightarrow2x=2\Rightarrow x=1\)

i) \(x^{50}=x\Rightarrow x^{50}-x=0\Rightarrow x\left(x^{49}-1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x^{49}-1=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0\\x^{49}=1=1^{49}\end{matrix}\right.\)  \(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

4ⁿ  =  4096 

4ⁿ = 2¹²

n = 12

5ⁿ = 15625 

5ⁿ = 5⁶

n   = 6

6ⁿ⁺³ = 216

6ⁿ⁺³ = 2³.3³

6ⁿ⁺³ = 6³

n + 3 = 3

A =    3.5.7.9.11 + 11.34

A = 11.(3.5.7.9 + 34)

A \(⋮\) 1;  11; A;  A > 11 ⇒ A là hợp số.

E = \(\left(16.64\right)^3.16^5.84^2\)

\(=16^3.64^3.16^5.84^2\)

\(=16^8.\left(4^3\right)^3.84^2\)

\(=4^{16}.4^9.7^2.12^2\)

\(=4^{16}.4^9.7^2.3^2.4^2\)

\(=4^{26}.49.9\)

a. A = 53. 571 = 53. (531 + 40) = 53. 531 + (53. 10). 4 = 53. 531 + 530. 4

B = 57. 531 = (53 + 4). 531 = 531. 53 + 531. 4 

Vì 530 < 531 => 53. 531 + 530. 4 < 531. 53 + 531. 4 hay A < B

b. X = 2011 x 2019 = 2011 x ( 2015 + 4) = 2011 x 2015 + 2011 x 4 

Y = 2015 x 2015 = ( 2011 + 4) x 2015 = 2011 x 2015 + 4 x 2015

Vì 2011 < 2015 

=> X < Y

A <b                                                     x<y

Số đĩa là UC(96; 60; 24)={2;3;4;6;12}

Do số đĩa >3 nên có cách cách chia

số đĩa ={4;6;12}

Cách chia nhiều đĩa nhất là

Số đĩa =UCLN (96;60;24}=12

Khi đó mỗi đia có

96:12=8 kẹo

60:12=5 bánh

24:12=2 hồng

8 kẹo

5 bánh

2 hồng

\(17^{100}=\left(17^4\right)^{25}\) có chữ số hàng đơn vị là 1

\(11^{2023}\) có chữ số hàng đơn vị là 1

\(3^{2023}=3^3.3^{2020}=3^3.\left(3^4\right)^{505}\) có chữ số hàng đơn vị là 7

=> A có chữ số hàng đơn vị là 3

là 3 nha

a) \(x-270:45=120\)

\(x-270=120.45\)

\(x-270=5400\)

\(x=5400+270\)

\(x=5670\)

_____

b) \(575-\left(6\times x+70\right)=445\)

\(6\times x+70=575-445\)

\(6\times x+70=130\)

\(6\times x=130-70\)

\(6\times x=60\)

\(x=60:6\)

\(x=10\)

_____

c) \(x-105:21=15\)

\(x-105=15.21\)

\(x-105=315\)

\(x=315+105\)

\(x=420\)

_____

d) \(3200:\left(405-x\right)=8\)

\(405-x=3200:8\)

\(405-x=400\)

\(x=405-400\)

\(x=5\)

_____

i) \(43575-75\times x=42450\)

\(75.x=43575-42450\)

\(75.x=1125\)

\(x=1125:75\)

\(x=15\)

_____

e) \(8,75\times x+1,25\times x=20\)

\(x\times\left(8,75+1,25\right)=20\)

\(x\times10=20\)

\(x=20:10\)

\(x=2\)

ko cần giải câu b đâu

\(\left(x+15\right):3=7\)

\(x+15=7.3\)

\(x+15=21\)

\(x=21-15\)

\(x=6\)

----------------------------------

\(4.\left(6-x\right)=280:36\)

\(4.\left(6-x\right)=\dfrac{70}{9}\)

\(6-x=\dfrac{70}{9}:4\)

\(6-x=\dfrac{35}{18}\)

\(x=6-\dfrac{35}{18}\)

\(x=\dfrac{73}{18}\)

----------------------------------

\(5x-3x-12=8\)

\(2x=8+12\)

\(2x=20\)

\(x=\dfrac{20}{2}\)

\(x=10\)

\(\left(x+15\right):3=7\\ \Rightarrow x+15=7.3=21\\ \Rightarrow x=21-15=6\)

\(4\left(6-x\right)=280:36\\ \Rightarrow4\left(6-x\right)=\dfrac{70}{9}\\ \Rightarrow6-x=\dfrac{70}{9}:4\\ \Rightarrow6-x=\dfrac{35}{18}\\ \Rightarrow x=6-\dfrac{35}{18}=\dfrac{73}{18}\)

\(5x-3x-12=8\\ \Rightarrow2x=8+12=20\\ \Rightarrow x=\dfrac{20}{2}=10\)

\(\left(x+15\right):3=7\)

\(x+15=7.3\)

\(x+15=21\)

\(x=21-15\)

\(x=6\)

_____

\(5x-3x-12=8\)

\(\Leftrightarrow2x-12=8\)

\(2x=8+12\)

\(2x=20\)

\(x=20:2\)

\(x=10\)

______

\(4.\left(6-x\right)=280:36\)

\(4.\left(6-x\right)=\dfrac{280}{36}\)

\(6-x=\dfrac{280}{36}.\dfrac{1}{4}\)

\(6-x=\dfrac{35}{18}\)

\(x=6-\dfrac{35}{18}\)

\(x=\dfrac{108}{18}-\dfrac{36}{18}\)

\(x=\dfrac{73}{18}\)

Lần sau để đúng môn học nhé bạn!