a: =>3^x=3^4*3=3^5

=>x=5

b: =>\(2^{x+1}=2^5\)

=>x+1=5

=>x=4

c: \(\Leftrightarrow3^{x+2-3}=3\)

=>x-1=1

=>x=2

d: \(\Leftrightarrow x^2=\dfrac{32}{2}=16\)

=>x=4 hoặc x=-4

e: (2x-1)^4=81

=>2x-1=3 hoặc 2x-1=-3

=>2x=4 hoặc 2x=-2

=>x=-1 hoặc x=2

f: (2x-6)^4=0

=>2x-6=0

=>x-3=0

=>x=3

a) \(3^x=81\cdot3\)

\(\Rightarrow3^x=3^4\cdot3\)

\(\Rightarrow3^x=3^5\)

\(\Rightarrow x=5\)

b) \(2^{x+1}=32\)

\(\Rightarrow2^{x+1}=2^5\)

\(\Rightarrow x+1=5\)

\(\Rightarrow x=4\)

c) \(3^{x+2}:27=3\)

\(\Rightarrow3^{x+2}:3^3=3\)

\(\Rightarrow3^{x+2-3}=3\)

\(\Rightarrow3^{x-1}=3\)

\(\Rightarrow x-1=1\)

\(\Rightarrow x=2\)

d) \(2x^2=32\)

\(\Rightarrow x^2=16\)

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

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

e) \(\left(2x-1\right)^4=81\)

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

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

\(\Rightarrow\left[{}\begin{matrix}2x=4\\2x=-2\end{matrix}\right.\)

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

f)  \(\left(2x-6\right)^4=0\)

\(\Rightarrow2x-6=0\)

\(\Rightarrow2x=6\)

\(\Rightarrow x=6:2\)

\(\Rightarrow x=3\)

\(a,3^x=81\cdot3\\ \Leftrightarrow3^x=3^4\cdot3\\ \Leftrightarrow3^x=3^5\\ \Leftrightarrow x=5\\ d,2^{x+1}=32\\ \Leftrightarrow x+1=5\\ \Leftrightarrow x=4\\ c,3^{x+2}:27=3\\ \Leftrightarrow3^{x+2}:3^3=3\\ \Leftrightarrow3^{x-1}=3\\ \Leftrightarrow x-1=1\\ \Leftrightarrow x=2\\ d,2x^2=32\\ \Leftrightarrow x^2=16\\ \Leftrightarrow\left[{}\begin{matrix}x=4\\x=-4\end{matrix}\right.\\ e,\left(2x-1\right)^4=81\\ \Leftrightarrow\left[{}\begin{matrix}2x-1=3\\2x-1=-3\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\\ f,\left(2x-6\right)^4=0\\ \Leftrightarrow2x-6=0\\ \Leftrightarrow x=3\)

a) =>  (2x -1)⁶  - (2x - 1)⁸ = 0  => (2x - 1)⁶ - (2x - 1)⁶.(2x - 1)² = 0 

=> (2x - 1)⁶.[1 - (2x - 1)²] = 0 => (2x - 1)⁶ =  0 hoặc 1 - (2x - 1)² = 0 

+) (2x - 1)⁶ = 0 => 2x - 1 = 0 => x = 1/2

+) 1 - (2x - 1)² = 0 => (2x - 1)² = 1 => 2x - 1 = 1 hoặc 2x - 1 = - 1

2x - 1 = 1 => x = 1

2x - 1 = - 1 => x = 0

Vậy x = 0 ; x = 1/2; x = 1

b) => 5^x + 5.5^x = 650

=> 6.5^x = 650 => 5^x = 650 : 6 = 325/3 => không có số x nào thỏa mãn

Vậy............ 

d, ( x+1) nhé. Mình viết nhầm

Trả lời nhanh hộ mình

a)\(\frac{x+11}{x-6}=\frac{x-6+17}{x-6}=\frac{x-6}{x-6}+\frac{17}{x-6}\)

=>x-6\(\in\) Ư(17)

Bài 1:

a/ \(\frac{x+11}{x-6}\)\(\varepsilon\)Z

= \(\frac{x-6+17}{x-6}\)

= \(\frac{x-6}{x-6}\)+ \(\frac{17}{x-6}\)

= \(1+\frac{17}{x-6}\)

\(\Rightarrow\frac{7}{x-6}\)\(\varepsilon\)Z \(\Leftrightarrow x-6\)\(\varepsilon\)\(Ư\left(7\right)\)

\(\Rightarrow x\)\(\varepsilon\)\(\left\{-1;5;7;13\right\}\)

b/ \(\frac{3x+5}{x-2}\)\(\varepsilon\)Z

= \(\frac{3x-6+11}{x-2}\)

= \(\frac{3\left(x-2\right)}{x-2}+\frac{11}{x-2}\)

=  \(3+\frac{11}{x-2}\)

\(\Rightarrow\frac{11}{x-2}\)\(\varepsilon\)Z \(\Leftrightarrow x-2\)\(\varepsilon\)\(Ư\left(11\right)\)

\(\Rightarrow x\)\(\varepsilon\)\(\left\{-5;1;3;9\right\}\)

c/  \(\frac{x^2+11}{x-5}\)\(\varepsilon\)Z

=  \(\frac{x^2-25+36}{x-5}\)

= \(\frac{\left(x+5\right)\left(x-5\right)}{x-5}+\frac{36}{x-5}\)

=  \(x+5+\frac{36}{x-5}\)

Ta có: \(x\)\(\varepsilon\)Z

\(\Rightarrow x+5\)\(\varepsilon\)Z

\(\Rightarrow\frac{36}{x-5}\)\(\varepsilon\)Z \(\Leftrightarrow x-5\)\(\varepsilon\)\(Ư\left(36\right)\)

\(\Rightarrow x\)\(\varepsilon\)\(\left\{-31;-7;-4;-1;1;2;3;4;6;7;8;9;11;14;17;41\right\}\)

a) \(3\dfrac{4}{5}:\dfrac{8}{5}=0,25:x\)

\(\Rightarrow\dfrac{19}{5}.\dfrac{5}{8}=\dfrac{x}{4}\)

\(\Rightarrow\dfrac{x}{4}=2\Rightarrow x=8\)

b) \(2x+\dfrac{3}{24}=3x-\dfrac{1}{32}\)

\(\Rightarrow x=\dfrac{1}{8}+\dfrac{1}{32}=\dfrac{5}{32}\)

c) \(\dfrac{13x-2}{2x+5}=\dfrac{76}{17}\)

\(\Rightarrow221x-34=152x+380\)

\(\Rightarrow69x=414\Rightarrow x=6\)