Câu hỏi của Gia Hân Bùi

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HT.Phong (9A5) · Accepted Answer

a) $\left(\dfrac{1}{3}\right)^m=\dfrac{1}{81}$$\Rightarrow\left(\dfrac{1}{3}\right)^m=\left(\dfrac{1}{3}\right)^4$$\Rightarrow m=4$b) $\dfrac{1}{9}\cdot27^n=3^n$$\Rightarrow\dfrac{1}{3^2}\cdot\left(3^3\right)^n=3^n$$\Rightarrow\dfrac{3^{3n}}{3^2}=3^n$$\Rightarrow3^{3n-2}=3^n$$\Rightarrow3n-2=n$$\Rightarrow2n=2$$\Rightarrow n=1$c) $\dfrac{8}{2^n}=2$$\Rightarrow\dfrac{2^3}{2^n}=2$$\Rightarrow2^{3-n}=2^1$$\Rightarrow3-n=1$$\Rightarrow n=2$d) $32^n\cdot16^{-n}=1024$$\Rightarrow\left(2^5\right)^n\cdot\left(2^4\right)^{-n}=2^{10}$$\Rightarrow2^{5n-4n}=2^{10}$$\Rightarrow2^n=2^{10}$$\Rightarrow n=10$e) $3^{-1}\cdot3^n+5\cdot3^{n-1}=162$$\Rightarrow3^{n-1}+5\cdot3^{n-1}=162$$\Rightarrow3^{n-1}\cdot6=162$$\Rightarrow3^{n-1}=27$$\Rightarrow3^{n-1}=3^3$$\Rightarrow n-1=3$$n=4$f) $\left(n-\dfrac{2}{3}\right)^3=\dfrac{1}{27}$$\Rightarrow\left(n-\dfrac{2}{3}\right)^3=\left(\dfrac{1}{3}\right)^3$$\Rightarrow n-\dfrac{2}{3}=\dfrac{1}{3}$$\Rightarrow n=\dfrac{1}{3}+\dfrac{2}{3}$$\Rightarrow n=1$Câu trả lời: a) $\left(\dfrac{1}{3}\right)^m=\dfrac{1}{81}$$\Rightarrow\left(\dfrac{1}{3}\right)^m=\left(\dfrac{1}{3}\right)^4$$\Rightarrow m=4$b) $\dfrac{1}{9}\cdot27^n=3^n$$\Rightarrow\dfrac{1}{3^2}\cdot\left(3^3\right)^n=3^n$$\Rightarrow\dfrac{3^{3n}}{3^2}=3^n$$\Rightarrow3^{3n-2}=3^n$$\Rightarrow3n-2=n$$\Rightarrow2n=2$$\Rightarrow n=1$c) $\dfrac{8}{2^n}=2$$\Rightarrow\dfrac{2^3}{2^n}=2$$\Rightarrow2^{3-n}=2^1$$\Rightarrow3-n=1$$\Rightarrow n=2$d) $32^n\cdot16^{-n}=1024$$\Rightarrow\left(2^5\right)^n\cdot\left(2^4\right)^{-n}=2^{10}$$\Rightarrow2^{5n-4n}=2^{10}$$\Rightarrow2^n=2^{10}$$\Rightarrow n=10$e) $3^{-1}\cdot3^n+5\cdot3^{n-1}=162$$\Rightarrow3^{n-1}+5\cdot3^{n-1}=162$$\Rightarrow3^{n-1}\cdot6=162$$\Rightarrow3^{n-1}=27$$\Rightarrow3^{n-1}=3^3$$\Rightarrow n-1=3$$n=4$f) $\left(n-\dfrac{2}{3}\right)^3=\dfrac{1}{27}$$\Rightarrow\left(n-\dfrac{2}{3}\right)^3=\left(\dfrac{1}{3}\right)^3$$\Rightarrow n-\dfrac{2}{3}=\dfrac{1}{3}$$\Rightarrow n=\dfrac{1}{3}+\dfrac{2}{3}$$\Rightarrow n=1$

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