85.
Đặt \(3^x=t>0\)
\(\Rightarrow t\le4-\dfrac{3}{t}\) \(\Rightarrow t^2-4t+3\le0\)
\(\Rightarrow1\le t\le3\Rightarrow1\le3^x\le3\)
\(\Rightarrow0\le x\le1\)
86.
\(\Leftrightarrow2^{2x}-2.2^x-8>0\)
\(\Leftrightarrow\left(2^x-4\right)\left(2^x+2\right)>0\)
\(\Leftrightarrow2^x>4\)
\(\Rightarrow x>2\)
88.
\(\Leftrightarrow6^2.6^x-6.6^x\le3^2.3^x-3.3^x\)
\(\Leftrightarrow30.6^x\le6.3^x\)
\(\Leftrightarrow2^x\le\dfrac{1}{5}\)
\(\Rightarrow x\le log_2\left(\dfrac{1}{5}\right)=-log_25\)
89.
\(6^x-2.3^x-2.2^x+4\le0\)
\(\Leftrightarrow3^x\left(2^x-2\right)-2\left(2^x-2\right)\le0\)
\(\Leftrightarrow\left(3^x-2\right)\left(2^x-2\right)\le0\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}3^x-2\le0\\2^x-2\ge0\end{matrix}\right.\\\left\{{}\begin{matrix}3^x-2\ge0\\2^x-2\le0\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\le log_32\\x\ge1\end{matrix}\right.\\\left\{{}\begin{matrix}x\ge log_32\\x\le1\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow log_32\le x\le1\Rightarrow\) có duy nhất 1 giá trị x nguyên
