a)

(2x-1)⁴ = 3⁴

=>2x-1 = 3

    2x     = 3+1

     2x     = 4

       x      = 2

b)

(3x-1)³ = 5³

=> 3x-1 = 5

      3x     = 5+1 

        3x     = 6

         x      = 2

c)

4^x-1 . 4²  = 4⁵

        4^x-1 = 4⁵ : 4²

        4^x-1 = 4³

=> x-1 = 3 

      x= 4

d)

3.3⁴  nhỏ hơn hoặc bằng 3^2x nhỏ hơn hoặc bằng 3³ . 3⁵

3⁵ nhỏ hơn hoặc bằng  3^2x  nhỏ hơn hoặc bằng 3⁸

=> 2x = 5 ; 6 ;7; 8

Nếu 2x = 5 thì x = 5:2 (loại)

Nếu 2x = 6 thì x = 3 ( thỏa mãn )

Nếu 2x = 7 thì x = 7: 2 ( loại)

Nếu 2x = 8 thì x = 4 ( thỏa mãn )

=> x= 3:4

a) \(\left(2x-1\right)^4=81\)

\(\left(2x-1\right)^4=3^4\)

\(\Rightarrow2x-1=3\)

\(\Rightarrow2x=4\)

\(\Rightarrow x=2\)

vay \(x=2\)

b) \(\left(3x-1\right)^3=125\)

\(\left(3x-1\right)^3=5^3\)

\(\Rightarrow3x-1=5\)

\(\Rightarrow3x=6\)

\(\Rightarrow x=2\)

vay \(x=2\)

c) \(4^{x-1}.16=1024\)

\(4^{x-1}=\frac{1024}{16}\)

\(4^{x-1}=64\)

\(4^{x-1}=4^3\)

\(\Rightarrow x-1=3\)

\(\Rightarrow x=4\)

vay \(x=4\)

d) \(3.81\le9^x\le27.243\)

\(3.3^4\le9^x\le3^3.3^5\)

\(3^5\le3^{2x}\le3^8\)

\(\Rightarrow5\le2x\le8\)

\(\Rightarrow\orbr{\begin{cases}2x\le8\\2x\ge5\end{cases}}\Rightarrow\orbr{\begin{cases}x\le4\\x\ge\frac{5}{2}\end{cases}}\Rightarrow\frac{5}{2}\le x\le8\)

   vay \(\frac{5}{2}\le x\le8\)

a)

\(\left(2x-1\right)^4=3^4\)

\(2x-1=3\)

\(2x=4\)

\(x=2\)

b)

\(\left(3x-1\right)^3=5^3\)

\(3x-1=5\)

\(3x=6\)

\(x=2\)

c)

\(4^{x-1}.4^2=4^5\)

\(\left(x-1\right)+2=4\)

\(x-1=2\)

\(x=3\)

a. x =2

b/ 6

c.1

d/1

tk nha

a : X= 2 , b : X = 6, c: X = 0 hoặc 1,d:x = 1

a) \(2\cdot5^x=50\)

\(\Leftrightarrow5^x=25\)

\(\Leftrightarrow5^x=5^2\)

\(\Leftrightarrow x=2\)

b) \(3^x:81=9\)

\(\Leftrightarrow3^x=729\)

\(\Leftrightarrow3^x=3^6\)

\(\Leftrightarrow x=6\)

c) \(x=x^{20}\Rightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}\)

d) \(\left(2x-1\right)^3=\left(2x-1\right)^4\)

\(\Leftrightarrow\left(2x-1\right)^3-\left(2x-1\right)^4=0\)

\(\Leftrightarrow\left(2x-1\right)^3\left(1-2x-1\right)=0\)

\(\Leftrightarrow-2x\left(2x-1\right)=0\)

\(\Rightarrow\orbr{\begin{cases}-2x=0\\2x-1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=0\\x=\frac{1}{2}\end{cases}}}\)

a) \(3^{a+1}=81\)

\(3^{a+1}=3^4\)

\(a+1=4\)

\(a=3\)

b) \(\left(x-1\right)^3=27\)

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

\(x-1=3\)

\(x=4\)

\(a,3^{a+1}=81\\ \Rightarrow3^{a+1}=3^4\\ \\ \Rightarrow a+1=4\\ \Rightarrow a=3.\\ b,\left(x-1\right)^3=27\\ \Rightarrow\left(x-1\right)^3=3^3\\ \Rightarrow x-1=3\\ \Rightarrow x=4.\)

\(\left(x+4\right)^2-81=0\Leftrightarrow\left(x+4\right)^2-9^2=0\)

\(\Leftrightarrow\left(x+4+9\right)\times\left(x+4-9\right)=0\)

\(\Leftrightarrow\left(x+13\right)\times\left(x-5\right)=0\)

\(\left[{}\begin{matrix}x+13=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-13\\x=5\end{matrix}\right.\)

a)(2x-1)2=81

x=20,75

b)x:(1/2)3=1/2

x=0,75

bn k cho mik nha!!!<3

a) 5^x=125

=> 5^x=5^2

=>x=2

b) 3^2*x=81

=>3^2*x=9^2

=>3^2*x=(3^2)^2

=>x=2

câu c chưa hiểu chỗ 5^2x3 hay 5^2*3 vậy ?

a) \(5^x=125\)

\(5^x=5^3\)

\(\Rightarrow x=3\)

b)\(3^{2x}=81\)

\(3^{2x}=3^4\)

\(\Rightarrow2x=4\)

\(x=4:2\)

\(x=2\)

c)\(5^{2x-3}-2.5^2=5^2.3\)

\(5^{2x-3}=5^2.3+5^2.2\)

\(5^{2x-3}=5^2.\left(3+2\right)\)

\(5^{2x-3}=5^3\)

\(\Rightarrow2x-3=3\)

\(2x=3+3\)

\(2x=6\)

\(x=6:2\)

\(x=3\)

5^2x3 nha

Để \(\dfrac{3}{\left|x\right|}>1\) thì \(\dfrac{3}{\left|x\right|}-1>0\)

=>\(\dfrac{3-\left|x\right|}{\left|x\right|}>0\)

=>\(3-\left|x\right|>0\)

=>\(\left|x\right|< 3\)

mà x nguyên và x<>0

nên \(x\in\left\{1;-1;2;-2\right\}\)

=>\(2x^2-1\in\left\{1;1;7;7\right\}\)

=>A={1;7}

\(1< =x^2< =81\)

mà \(x\in\)N^*

nên \(x^2\in\left\{1;4;9;16;25;36;49;64;81\right\}\)

=>\(x\in\left\{1;2;3;4;5;6;7;8;9\right\}\)

=>B={1;2;3;4;5;6;7;8;9}

A={1;7}; B={1;2;3;4;5;6;7;8;9}

\(C_AB=A\text{B}=\varnothing\)

=>\(X=\varnothing\)

=>Tập X không có phần tử nào là số nguyên tố

a. (2x-1)⁴=81

=>(2x-1)⁴=3⁴

=>2x-1=3

=>2x=3+1

=>2x=4

=>x=4:2

=>x=2

b.(x-1)⁵=-32

=>(x-1)⁵=(-2)⁵

=>x-1=-2

=>x=-2+1

=>x=-1

c.(2x-1)⁶=(2x-1)⁸

mà chỉ có: (-1)⁶=(-1)⁸; 0⁶=0⁸; 1⁶=1⁸

=> để (2x-1) \(\in\){-1;0;1} thì x \(\in\){0; 1/2; 1}

(2x-1)^4=3^4

=>2x-1=3

=>2x=4

=>x=2

ai h minh minh h lai cho