Câu hỏi của Ely Christina

Question

Mình cần gấp cả 2 bài ạ. cảm ơn

Đoàn Đức Hà · Accepted Answer

2) So sánh: a) $3^{24}=\left(3^6\right)^4=729^4< 3125^4=\left(5^5\right)^4=5^{20}$c) $\left(\frac{1}{2}\right)^{300}=\left(\frac{1}{2^3}\right)^{100}=\left(\frac{1}{8}\right)^{100}>\left(\frac{1}{9}\right)^{100}=\left(\frac{1}{3^2}\right)^{100}=\left(\frac{1}{3}\right)^{200}$b) $17^{20}=\left(17^4\right)^5>\left(3^4\right)^5=81^5>71^5$d) $\left(\frac{1}{3}\right)^{75}=\left(\frac{1}{3^3}\right)^{25}=\left(\frac{1}{27}\right)^{25}< \left(\frac{1}{25}\right)^{25}=\left(\frac{1}{5^2}\right)^{25}=\left(\frac{1}{5}\right)^{50}$e) $2^{27}=\left(2^3\right)^9=8^9< 9^9=\left(3^2\right)^9=3^{18}$g) $32^9=\left(2^5\right)^9=2^{45}=2^{13}.2^{32}=2^{13}.\left(2^4\right)^8=2^{13}.16^8< 2^{13}.27^8=2^{13}.3^{24}$$< 2^{13}.3^{26}=\left(2.3^2\right)^{13}=18^{13}$Câu trả lời: 2) So sánh: a) $3^{24}=\left(3^6\right)^4=729^4< 3125^4=\left(5^5\right)^4=5^{20}$c) $\left(\frac{1}{2}\right)^{300}=\left(\frac{1}{2^3}\right)^{100}=\left(\frac{1}{8}\right)^{100}>\left(\frac{1}{9}\right)^{100}=\left(\frac{1}{3^2}\right)^{100}=\left(\frac{1}{3}\right)^{200}$b) $17^{20}=\left(17^4\right)^5>\left(3^4\right)^5=81^5>71^5$d) $\left(\frac{1}{3}\right)^{75}=\left(\frac{1}{3^3}\right)^{25}=\left(\frac{1}{27}\right)^{25}< \left(\frac{1}{25}\right)^{25}=\left(\frac{1}{5^2}\right)^{25}=\left(\frac{1}{5}\right)^{50}$e) $2^{27}=\left(2^3\right)^9=8^9< 9^9=\left(3^2\right)^9=3^{18}$g) $32^9=\left(2^5\right)^9=2^{45}=2^{13}.2^{32}=2^{13}.\left(2^4\right)^8=2^{13}.16^8< 2^{13}.27^8=2^{13}.3^{24}$$< 2^{13}.3^{26}=\left(2.3^2\right)^{13}=18^{13}$

Đoàn Đức Hà · Answer

3) Tìm $x$, biết: a) $\left(\frac{3}{4}\right)^x=\frac{2^8}{3^4}$$\Leftrightarrow\left(\frac{3}{4}\right)^x=\left(\frac{4}{3}\right)^4$$\Leftrightarrow\left(\frac{3}{4}\right)^x=\left(\frac{3}{4}\right)^{-4}$$\Leftrightarrow x=-4$b) $\left(x-2\right)^8=\left(x-2\right)^6$$\Leftrightarrow\left(x-2\right)^6\left[\left(x-2\right)^2-1\right]=0$$\Leftrightarrow\orbr{\begin{cases}x-2=0\\left(x-2\right)^2=1\end{cases}}$$\Leftrightarrow\orbr{\begin{cases}x=2\x=3,x=1\end{cases}}$.c) $\left(1,78^{2x-2}-1,78^x\right)\div1,78^x=0$$\Leftrightarrow1,78^{x-2}-1=0$$\Leftrightarrow1,78^{x-2}=1,78^0$$\Leftrightarrow x-2=0$$\Leftrightarrow x=2$.d) $5^{\left(x-2\right)\left(x+3\right)}=1$$\Leftrightarrow\left(x-2\right)\left(x+3\right)=0$$\Leftrightarrow\orbr{\begin{cases}x-2=0\x+3=0\end{cases}}$$\Leftrightarrow\orbr{\begin{cases}x=2\x=-3\end{cases}}$e) $2021^{x^2+3x-4}=1$$\Leftrightarrow x^2+3x-4=0$$\Leftrightarrow\left(x+4\right)\left(x-1\right)=0$$\Leftrightarrow\orbr{\begin{cases}x+4=0\x-1=0\end{cases}}$$\Leftrightarrow\orbr{\begin{cases}x=-4\x=1\end{cases}}$Câu trả lời: 3) Tìm $x$, biết: a) $\left(\frac{3}{4}\right)^x=\frac{2^8}{3^4}$$\Leftrightarrow\left(\frac{3}{4}\right)^x=\left(\frac{4}{3}\right)^4$$\Leftrightarrow\left(\frac{3}{4}\right)^x=\left(\frac{3}{4}\right)^{-4}$$\Leftrightarrow x=-4$b) $\left(x-2\right)^8=\left(x-2\right)^6$$\Leftrightarrow\left(x-2\right)^6\left[\left(x-2\right)^2-1\right]=0$$\Leftrightarrow\orbr{\begin{cases}x-2=0\\left(x-2\right)^2=1\end{cases}}$$\Leftrightarrow\orbr{\begin{cases}x=2\x=3,x=1\end{cases}}$.c) $\left(1,78^{2x-2}-1,78^x\right)\div1,78^x=0$$\Leftrightarrow1,78^{x-2}-1=0$$\Leftrightarrow1,78^{x-2}=1,78^0$$\Leftrightarrow x-2=0$$\Leftrightarrow x=2$.d) $5^{\left(x-2\right)\left(x+3\right)}=1$$\Leftrightarrow\left(x-2\right)\left(x+3\right)=0$$\Leftrightarrow\orbr{\begin{cases}x-2=0\x+3=0\end{cases}}$$\Leftrightarrow\orbr{\begin{cases}x=2\x=-3\end{cases}}$e) $2021^{x^2+3x-4}=1$$\Leftrightarrow x^2+3x-4=0$$\Leftrightarrow\left(x+4\right)\left(x-1\right)=0$$\Leftrightarrow\orbr{\begin{cases}x+4=0\x-1=0\end{cases}}$$\Leftrightarrow\orbr{\begin{cases}x=-4\x=1\end{cases}}$

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