20.
ĐKXĐ: \(0< x< 1\)
\(log_2\left(log_{\dfrac{1}{3}}x\right)< 3\)
\(\Leftrightarrow log_{\dfrac{1}{3}}x< 2^3=8\)
\(\Rightarrow x>\left(\dfrac{1}{3}\right)^8=\dfrac{1}{3^8}\)
Kết hợp ĐKXĐ \(\Rightarrow\dfrac{1}{3^8}< x< 1\)
21.
ĐKXĐ: \(x< 0\)
\(log_{\dfrac{5}{6}}\left(log_3\left(1-x\right)\right)\ge1\)
\(\Leftrightarrow0< log_3\left(1-x\right)\le\dfrac{5}{6}\)
\(\Leftrightarrow1-x\le3^{\dfrac{5}{6}}\)
\(\Rightarrow x\ge1-3^{\dfrac{5}{6}}\)
Kết hợp ĐKXĐ \(\Rightarrow1-3^{\dfrac{5}{6}}\le x< 0\)
a) \(\log_2\left(\log_{\dfrac{1}{3}}x\right)< 3\)
Điều kiện:
\(\left\{{}\begin{matrix}x>0\\\log_{\dfrac{1}{3}}x>0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x>0\\x< 1\end{matrix}\right.\) \(\Leftrightarrow0< x< 1\)
Phương trình tương đương:
\(\log_2\left(\log_{\dfrac{1}{3}}x\right)< 3\)
\(\Leftrightarrow\log_{\dfrac{1}{3}}x< 8\)
\(\Leftrightarrow x>\left(\dfrac{1}{3}\right)^8\)
\(\Leftrightarrow x>\dfrac{1}{6561}\) (loại)
