\(A=4.\left(3^2+1\right).\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)

\(=\frac{1}{2}\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)

\(=\frac{1}{2}\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)

\(=\frac{1}{2}\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)

\(=\frac{1}{2}\left(3^{16}-1\right)\left(3^{16}+1\right)\)

\(=\frac{3^{32}-1}{2}< 3^{32}-1=B\)

Vậy \(A< B\)

a) 1 + 1/4 + 1/8 + 1/16

= 16/16 + 4/16 + 2/16 + 1/16

= 23/16

b) 2 - 1/8 - 1/12 - 1/16

= 96/48 - 6/46 - 4/48 - 3/48

= 83/48

c) 4/99 × 18/5 : 12/11 + 3/5

= 8/55 : 12/11 + 3/5

= 2/15 + 3/5

= 2/15 + 9/15

= 11/15

d) (1 - 3/4) × (1 + 1/3) : (1 - 1/3)

= 1/4 × 4/3 : 2/3

= 1/3 : 2/3

= 2

1 + 1/4 + 1/8 + 1/16

= 16 + 4 + 2 + 1 / 16

=23/16

2-1/8-1/12-1/16

= 96 - 6 - 4 - 3 / 48

= 83 / 48

4/99 x 18/5 : 12 /11 + 3/5

= 4/99 x 18/5 x 11/12 + 3/5

= 2/15 + 3/5

= 11/15

(1 - 3/4) x (1+1/3) : (1-1/3) 

= 1/4 x 4/3 : 2/3

= 1/4 x 4/3 x 3/2

= 1/2

a) => \(\left(\frac{1}{3}-\frac{5}{6}x\right)^3=\frac{5}{6}-\frac{21}{54}=\frac{24}{54}=\frac{4}{9}\)

=> \(\frac{1}{3}-\frac{5}{6}x=\sqrt[3]{\frac{4}{9}}\) => \(\frac{5}{6}x=\frac{1}{3}-\sqrt[3]{\frac{4}{9}}\) => \(x=\frac{6}{5}.\left(\frac{1}{3}-\sqrt[3]{\frac{4}{9}}\right)\)

b) \(\frac{1}{3}\left(\frac{1}{2}x-1\right)^4=\frac{1}{12}-\frac{1}{16}=\frac{1}{48}\) => \(\left(\frac{1}{2}x-1\right)^4=\frac{3}{48}=\frac{1}{16}\)

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

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

c) \(\left(1+5\right).\left(\frac{3}{5}\right)^{x-1}=\frac{54}{25}\) => \(\left(\frac{3}{5}\right)^{x-1}=\frac{9}{25}=\left(\frac{3}{5}\right)^2\)

=> x - 1= 2 => x = 3

d) \(\left(1+\left(\frac{2}{3}\right)^2\right).\left(\frac{2}{3}\right)^x=\frac{101}{243}\) => \(\frac{13}{9}.\left(\frac{2}{3}\right)^x=\frac{101}{243}\)

=> \(\left(\frac{2}{3}\right)^x=\frac{101}{243}:\frac{13}{9}=\frac{101}{351}\) (có lẽ đề sai)

2) \(\frac{1}{27^{11}}=\frac{1}{\left(3^3\right)^{11}}=\frac{1}{3^{33}}\); \(\frac{1}{81^8}=\frac{1}{\left(3^4\right)^8}=\frac{1}{3^{32}}\)

Vì 3³³ > 3³² => \(\frac{1}{3^{33}}\) < \(\frac{1}{3^{32}}\) => \(\frac{1}{27^{11}}\) < \(\frac{1}{81^8}\)

b) \(\frac{1}{3^{99}}=\frac{1}{\left(3^3\right)^{33}}=\frac{1}{27^{33}}

nhjeu wa bạn giải 1 mjk luôn đi

Bạn nên viết đề bằng công thức toán và ghi đầy đủ yêu cầu đề để mọi người hiểu đề của bạn hơn nhé.

Câu 1 :

a, 8.( -5 ).( -4 ).2

= [ 8.2 ].[( -5 ).(-4 ]

= 16.20

= 320

b, \(1\frac{3}{7}+\frac{-1}{3}+2\frac{4}{7}\)

\(=\frac{10}{7}+\frac{-1}{3}+\frac{18}{7}\)

\(=\frac{11}{3}\)

c, \(\frac{8}{5}.\frac{2}{3}+\frac{-5.5}{3.5}\)

\(=\frac{8}{3}+\frac{-5}{3}\)

\(=\frac{3}{3}=1\)

d, \(\frac{6}{7}+\frac{5}{8}:5-\frac{3}{16}.\left(-2\right)^2\)

\(=\frac{6}{7}+\frac{1}{8}-\frac{3}{16}.4\)

\(=\frac{55}{56}-\frac{3}{4}\)

\(=\frac{13}{56}\)

Câu 2 :

a, 2x + 10 = 16

    2x = 16 + 10

    2x = 26

    x = 26 : 2

    x = 13

b, \(x-\frac{1}{3}=\frac{5}{4}\)

\(x=\frac{5}{4}+\frac{1}{3}\)

\(x=\frac{19}{12}\)

c, \(2x+3\frac{1}{3}=7\frac{1}{3}\)

\(2x+\frac{10}{3}=\frac{22}{3}\)

\(2x=\frac{22}{3}-\frac{10}{3}\)

\(2x=4\)

\(x=4:2\)

\(x=2\)

d, \(\left(\frac{2}{11}+\frac{1}{3}\right)x=\left(\frac{1}{7}-\frac{1}{8}\right).56\)

\(\frac{17}{33}x=1\)

\(x=1-\frac{17}{33}\)

\(x=\frac{16}{33}\)

a) 64 * 4^x = 16^8

          4^x = 16^8 : 64

          4^x = 2^32 : 2^6

          4^x = 2^26

          4^x = (2^2)13

          4^x = 4^13

=> x= 13

b) (2x+1)^3 = 5^3

=> 2x+1 = 5

     2x = 4

       x= 2

c) (x-5)^4 =(x-5)^6

d) (x-1)^x+2 = (x-1)^x+4

   (x-1)^x * (x-1)^2 = (x-1)^x * (x-1)^4

   (x-1)^x = (x-1)^4 :(x-2)^2

   (x-1)^x = (x-2)^2 

=> x=2

bạn giúp mình giải luôn bài 1 tính đc hông zợ ???

a, \(\frac{x+1}{5}=\frac{3}{7}\Rightarrow7\left(x+1\right)=15\Rightarrow7x+7=15\Rightarrow7x=8\Rightarrow x=\frac{8}{7}\)

b, \(\frac{x-2}{3}=\frac{3}{8}\Rightarrow8\left(x-2\right)=9\Rightarrow8x-16=9\Rightarrow8x=25\Rightarrow x=\frac{25}{8}\)

c, \(\frac{-x-1}{2}=\frac{-3}{5}\Rightarrow5\left(-x-1\right)=-6\Rightarrow-5x-5=-6\Rightarrow-5x=-1\Rightarrow x=\frac{1}{5}\)

d, \(\frac{4}{5-x}=\frac{1}{3}\Rightarrow5-x=12\Rightarrow x=-7\)

e, \(2x\left(x-\frac{1}{7}\right)=0\Rightarrow\orbr{\begin{cases}2x=0\\x-\frac{1}{7}=0\end{cases}\Rightarrow\orbr{\begin{cases}x=0\\x=\frac{1}{7}\end{cases}}}\)

\(\left(\frac{-7}{4}:\frac{5}{8}\right)\cdot\frac{11}{16}=\frac{-7}{4}\cdot\frac{8}{5}\cdot\frac{11}{16}=\frac{-7.11}{4.5.2}=\frac{-77}{40}\)

a) x+1/5=3/7

   x=3/7-1/5

   x=8/7

Vậy....

a) (2^x)⁵ : 4³ = 8¹⁵ => 2^5x = 8¹⁵.4³ = (2³)¹⁵.(2²)³ = 2⁴⁵.2⁶ = 2⁵¹ => 5x = 51 => x = 10,2 

b) (3²)^x .9³ = 243⁹ => 3^2x = 243⁹ : 9³ = (3⁵)⁹ : (3²)³ = 3⁴⁵ : 3⁶ = 3³⁹ => 2x = 39 => x = 19,5

c) (1/125)³.5^x = 25⁵ => 5^x = 25⁵ : (1/125)³ = (5²)⁵ : (1/5³)³ = 5¹⁰ : (5^-3)³ = 5¹⁰ : 5^-9 = 5¹⁹ => x = 19

d) 1/81 : 3^x = 1/729 => 3^x = 1/81 : 1/729 = 1/3⁴.729 = 3^-4.3⁶ = 3² => x = 2

e) (5x - 2)⁴ = 16⁸ = (16²)⁴ = 256⁴

=> 5x - 2 = -256 ; 256 => 5x = -254 ; 258 => x = -50,8 ; 51,6

P/S : Thay x = 10,2 vào câu a , x = 19,5 vào câu b sẽ thấy điều hư cấu : 2^10,2 và 9^19,5.Ko thể tính được giá trị của 2 lũy thừa này.

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