Để tớ ghi đề giùm cho các bạn hiểu :

\(11^{21}+1\div11=121\)

\(4^{2x}+1=64\)

So sánh

\(10^{30}...2^{100}\)

\(2^{98}...9^{42}\)

bài 1

4^2x+1 = 64

=> 4^2x+1 = 4³

=> 2x + 1 = 3

=> 2x = 2

=> x = 1

bài 2

10³⁰ = ( 10³ )¹⁰ = 1000¹⁰

2¹⁰⁰ = ( 2¹⁰ )¹⁰ = 1024¹⁰

=> 1000¹⁰ < 1024¹⁰

=> 10³⁰ < 2¹⁰⁰

2⁹⁸ = ( 2⁷ )¹⁴ = 128¹⁴

9⁴² = ( 9³ )¹⁴ = 729¹⁴

=> 128¹⁴ < 729¹⁴

=> 2⁹⁸ < 9⁴²

a. \(12^2.3^2.2^3=2^4.3^2.3^2.2^3=2^7.3^4\)

b. \(8^3.3^2.6^3=2^9.3^2.2^3.3^3=2^{12}.3^5\)

c. \(5^{32}.5^2=5^{34}\)

d. \(100^6.2^3=\left(2^2.5^2\right)^6.2^3=2^8.5^8.2^3=2^{11}.5^8\)

e. \(100^2:10^2:5^2=\left(10.5.2\right)^2:10^2:5^2=2^2\)

f. \(121^3-11^2=11^6-11^2=11^2\left(11^4-1\right)\)

cho mình hỏi mũ là gì

+) \(x^2=121\)

\(\Rightarrow\orbr{\begin{cases}x^2=11^2\\x^2=\left(-11\right)^2\end{cases}}\Rightarrow\orbr{\begin{cases}x=11\\x=-11\end{cases}}\)

Vậy x = 11 hoặc x = -11

+) \(2^{x+3}=1024\)

\(\Rightarrow2^{x+3}=2^{10}\)

\(\Rightarrow x+3=10\)

\(\Rightarrow x=10-3\)

\(\Rightarrow x=7\)

Vậy x = 7

+) \(5^{x+1}=625\)

\(\Rightarrow5^{x+1}=5^4\)

\(\Rightarrow x+1=4\)

\(\Rightarrow x=4-1\)

\(\Rightarrow x=3\)

Vậy x = 3

_Chúc bạn học tốt_

x^2 = 121

=> x = 11

2^(x+3)=1024

=> x+3=10

x=10-3

x=7

5^ ( x+1) = 625

=> x+1 = 4 

x=3

\(x^2=121\)

\(x^2=11^2\)

\(\Rightarrow x=11\)

Vậy \(x=11\)

\(2^{x+3}=1024\)

\(2^{x+3}=2^{10}\)

\(x+3=10\)

\(x=10-3\)

\(x=7\)

Vậy \(x=7\)

\(5^{x+1}=625\)

\(5^{x+1}=5^4\)

\(x+1=4\)

\(x=4-1\)

\(x=3\)

Vậy \(x=3\)

\(318-5\left(x-64\right)=103\)

\(\Rightarrow5\left(x-64\right)=318-103\)

\(\Rightarrow5\left(x-64\right)=215\)

\(\Rightarrow x-64=43\)

\(\Rightarrow x=43+64\)

\(\Rightarrow x=107\)

_____________

\(4^x\cdot5+216=296\)

\(\Rightarrow4^x\cdot5=296-216\)

\(\Rightarrow4^x\cdot5-80\)

\(\Rightarrow4^x=16\)

\(\Rightarrow4^x=4^2\)

\(\Rightarrow x=2\)

___________

\(376-6^x:3=364\)

\(\Rightarrow6^x:3=376-364\)

\(\Rightarrow6^x:3=12\)

\(\Rightarrow6^x=36\)

\(\Rightarrow6^x=6^2\)

\(\Rightarrow x=2\)

___________

\(\left(4x-1\right)^2=121\)

\(\Rightarrow\left(4x-1\right)^2=11^2\)

\(\Rightarrow\left[{}\begin{matrix}4x-1=11\\4x-1=-11\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}4x=12\\4x=-10\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{5}{2}\end{matrix}\right.\)

107

2

2

TH1: 3; TH2: -5/2

(2x+3)^2=(3/11)^2
=> 2x+3=3/11
2x = 3/11 - 3
2x = -30/11
x = -30/11 : 2
x = -15/11

mik nhầm. có 2 TH xảy ra nha bạn.
TH1: 2x+3 = 3/11
TH2: 2x+3 = -3/11

bạn có thể giair lại cho chính xác được không thank nhé

\(2^{121}>3^{81}\)

1.

a) \(x^3-\frac{1}{2}=\left(-\frac{3}{8}\right)\)

\(\Rightarrow x^3=\left(-\frac{3}{8}\right)+\frac{1}{2}\)

\(\Rightarrow x^3=\frac{1}{8}\)

\(\Rightarrow x^3=\left(\frac{1}{2}\right)^3\)

\(\Rightarrow x=\frac{1}{2}\)

Vậy \(x=\frac{1}{2}.\)

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

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

\(\Rightarrow2x-1=-2\)

\(\Rightarrow2x=\left(-2\right)+1\)

\(\Rightarrow2x=-1\)

\(\Rightarrow x=\left(-1\right):2\)

\(\Rightarrow x=-\frac{1}{2}\)

Vậy \(x=-\frac{1}{2}.\)

c) \(17+3^x=98\)

\(\Rightarrow3^x=98-17\)

\(\Rightarrow3^x=81\)

\(\Rightarrow3^x=3^4\)

\(\Rightarrow x=4\)

Vậy \(x=4.\)

Chúc bạn học tốt!

\(B=2^2+2^3+2^4+...+2^{121}\\=(2^2+2^3)+(2^4+2^5)+(2^6+2^7)+...+(2^{120}+2^{121})\\=2^2\cdot(1+2)+2^4\cdot(1+2)+2^6\cdot(1+2)+...+2^{120}\cdot(1+2)\\=2^2\cdot3+2^4\cdot3+2^6\cdot3+...+2^{120}\cdot3\\=3\cdot(2^2+2^4+2^6+...+2^{120})\)

Vì \(3\cdot(2^2+2^4+2^6+...+2^{120})\vdots3\)

nên \(B\vdots3\)