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1) \(5^{199}< 5^{200}=25^{100}\)

\(3^{300}=27^{100}>25^{100}\)

\(\Rightarrow3^{300}>5^{199}\)

\(\Rightarrow\dfrac{1}{3^{300}}< \dfrac{1}{5^{199}}\)

2)  a) \(107^{50}=\left(107^2\right)^{25}=11449^{25}\)

\(73^{75}=\left(73^3\right)^{25}=389017^{25}>11449^{25}\)

\(\Rightarrow107^{50}< 73^{75}\)

b) \(54^4< 5^{12}< 21^{12}\Rightarrow54^4< 21^{12}\)

Giúp mình với

Ta có: 

A = \(\dfrac{10^7+5}{10^7-8}=\dfrac{10^7-8+13}{10^7-8}=1+\dfrac{13}{10^7-8}\)

\(B=\dfrac{10^8+6}{10^8-7}=\dfrac{10^8-7+13}{10^8-7}=1+\dfrac{13}{10^8-7}\)

Mà \(10^8-7>10^7-8\)

=> \(1+\dfrac{13}{10^7-8}>1+\dfrac{13}{10^8-7}\)

=> A < B 

Vậy A < B

Xin lỗi mình kết luận sai vì nhìn nhầm. Đáp án đúng là A > B và cả quá trình trên vẫn đúng nha.

THAM KHẢO :

A = 53.107 + 54 53 + 1 .107 − 53

= 53.107 + 54 53.107 + 107 − 53

= 53.107 + 54 53.107 + 54 = 1.

B = 134.269 + 135 134 + 1 .269 − 133

= 134.269 + 135 134.269 + 269 − 133

= 134.269 + 135 134.269 + 136 > 1

⇒A < B 

A=B

Bài 1:

a: \(10^{10}=\left(2\cdot5\right)^{10}=2^{10}\cdot5^{10}=2^9\cdot5^{10}\cdot2\)

\(48\cdot50^5=2^4\cdot3\cdot\left(2\cdot5^2\right)^5=2^4\cdot3\cdot2^5\cdot5^{10}=2^9\cdot5^{10}\cdot3\)

mà 2<3

nên \(10^{10}<48\cdot50^5\)

b: \(1990^{10}+1990^9=1990^9\left(1990+1\right)=1990^9\cdot1991\)

\(1991^{10}=1991^9\cdot1991\)

mà 1990<1991

nên \(1990^{10}+1990^9<1991^{10}\)

c: \(107^{50}<108^{50}=\left(2^2\cdot3^3\right)^{50}=2^{100}\cdot3^{150}\)

\(73^{75}>72^{75}=\left(2^3\cdot3^2\right)^{75}=2^{225}\cdot3^{150}\)

mà \(2^{225}\cdot3^{150}>2^{100}\cdot3^{150}=108^{50}>107^{50}\)

nên \(73^{75}>107^{50}\)

d: \(2^{91}=\left(2^{13}\right)^7=8192^7\)

\(5^{35}=\left(5^5\right)^7=3125^7\)

mà 8192>3125

nên \(2^{91}>5^{35}\)

e: \(A=72^{45}-72^{44}=72^{44}\left(72-1\right)=72^{44}\cdot71\)

\(B=72^{44}-72^{43}=72^{43}\left(72-1\right)=72^{43}\cdot71\)

mà 44>43

nên A>B

Bài 2:

a:

ĐKXĐ: x<>2023

\(\frac{x-2023}{4}=\frac{1}{x-2023}\)

=>\(\left(x-2023\right)\left(x-2023\right)=4\cdot1\)

=>\(\left(x-2023\right)^2=4\)

=>\(\left[\begin{array}{l}x-2023=2\\ x-2023=-2\end{array}\right.\Rightarrow\left[\begin{array}{l}x=2+2023=2025\left(nhận\right)\\ x=-2+2023=2021\left(nhận\right)\end{array}\right.\)

b: \(\left(2x+1\right)^4=\left(2x+1\right)^6\)

=>\(\left(2x+1\right)^6-\left(2x+1\right)^4=0\)

=>\(\left(2x+1\right)^4\cdot\left\lbrack\left(2x+1\right)^2-1\right\rbrack=0\)

=>\(\left(2x+1\right)^4\cdot\left(2x+1-1\right)\left(2x+1+1\right)=0\)

=>\(2x\left(2x+1\right)^4\cdot\left(2x+2\right)=0\)

=>\(\left[\begin{array}{l}2x=0\\ 2x+1=0\\ 2x+2=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=-\frac12\\ x=-1\end{array}\right.\)

c: \(\left(3x-1\right)^{10}=\left(3x-1\right)^{20}\)

=>\(\left(3x-1\right)^{20}-\left(3x-1\right)^{10}=0\)

=>\(\left(3x-1\right)^{10}\cdot\left\lbrack\left(3x-1\right)^{10}-1\right\rbrack=0\)

=>\(\left[\begin{array}{l}\left(3x-1\right)^{10}=0\\ \left(3x-1\right)^{10}-1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}3x-1=0\\ \left(3x-1\right)^{10}=1\end{array}\right.\)

=>\(\left[\begin{array}{l}3x-1=0\\ 3x-1=1\\ 3x-1=-1\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac13\\ x=\frac23\\ x=0\end{array}\right.\)

d: Sửa đề \(2^{x+1}\cdot3^{y}=12^{x}\)

=>\(2^{x+1}\cdot3^{y}=\left(2^2\cdot3\right)^{x}=2^{2x}\cdot3^{x}\)

=>\(\begin{cases}2x=x+1\\ y=x\end{cases}\Rightarrow\begin{cases}x=1\\ y=x=1\end{cases}\)

Cô làm đ

107+5/107-8 -1=13/107-8

108+6/108-7 -1=13/108-7

Ta thấy 13/107-8>13/108-7=> 107+5/107-8>108+6/108-7

giúp mik nhé

PT 6 là chưa hợp lí. Oxit Fe khi tác dụng với HNO₃ thì sp khử chỉ có thể là NO₂ hoặc NO.

Cân bằng các phương trình sau:

Bài 1:

1.6 P + 5KClO3 → 3P2O5 + 5KCl.
2. 2P + 5H2 SO4 → 2H3PO4 + 5SO2 +2H2O.
3. S+ 2HNO3 → H2SO4 + 2NO.
4. 3C3H8 + 20HNO3 → 9CO2 + 20NO + 22H2O.
5. 3H2S + 4HClO3 → 4HCl +3H2SO4.
6. 5H2SO4 + C 2H2 → 2CO2 +5SO2 + 6H2O

Bài 2:.

3Mg + 8HNO3 → 3Mg(NO3)2 + NO + 4H2O.
2. 2Fe + 6H2SO4 → Fe2(SO4)3 + 3SO2 + 6H2O.
3. 4Mg + 5H2SO4 → 4MgSO4 + H2S + 4H2O.
4. 8Al + 30HNO3 → 8Al(NO3)3 + 3NH4NO3 + 9H2O.
5. 2FeCO3 + 4H2SO4 → Fe2(SO4)3 + SO2 + 2CO2 + 4H2O.
6. 8Fe3O4 + 74HNO3 → 24Fe(NO3)3 + N2O + 37H2O.
7.8 Al + 30HNO3 → 8Al(NO3)3 + 3N2O + 15H2O.
8. 2KMnO4 + 16HCl→ 2KCl + 2MnCl2 + 5Cl2 + 8H2O.
9. K2Cr2O7 + 14HCl→ 2KCl + 2CrCl3 + 3Cl2 + 7H2O

so sánh

a) 99²⁰ và 9999¹⁰

Ta có: 99²⁰=(99²)¹⁰=9801¹⁰

Vì 9801<9999

=> 9801¹⁰<9999¹⁰

Vậy 99²⁰<9999¹⁰