Question

[Ely Christina]

Mình cần gấp cả 2 bài ạ. cảm ơn

Answer 1

[Đoàn Đức Hà]

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) \(32^9=\left(2^5\right)^9=2^{45}=2^{13}.2^{32}=2^{13}.\left(2^4\right)^8=2^{13}.16^8< 2^{13}.27^8=2^{13}.3^{24}\)

\(< 2^{13}.3^{26}=\left(2.3^2\right)^{13}=18^{13}\)

Answer 2

[Đoàn Đức Hà]

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) \(2021^{x^2+3x-4}=1\)

\(\Leftrightarrow x^2+3x-4=0\)

\(\Leftrightarrow\left(x+4\right)\left(x-1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x+4=0\\x-1=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=-4\\x=1\end{cases}}\)