Chời, mắt toi bị lé hay sao mà ko thấy câu 2 luôn :v
\(DKXD:\dfrac{x-1}{2x-3}>0\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1>0\\2x-3>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-1< 0\\2x-3< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>\dfrac{3}{2}\\x< 1\end{matrix}\right.\)
\(\Rightarrow D=\left(-\infty;1\right)\cup\left(\dfrac{3}{2};+\infty\right)\)
\(y'=\dfrac{\left(\dfrac{x-1}{2x-3}\right)'}{\dfrac{x-1}{2x-3}.ln10}=\dfrac{\dfrac{2x-3-2x+2}{\left(2x-3\right)^2}}{\dfrac{x-1}{2x-3}.ln10}=\dfrac{-1}{\left(2x-3\right)\left(x-1\right).ln10}=...\)
\(\log_ab=3\Leftrightarrow a^3=b\)
\(\log_ab-\log_ac=\log_a\dfrac{b}{c}=3+2=5\Leftrightarrow a^5=\dfrac{b}{c}\Leftrightarrow c=\dfrac{b}{a^5}=\dfrac{a^3}{a^5}=\dfrac{1}{a^2}\)
\(\log_ax=k\Rightarrow\log_a\dfrac{b}{x}=3-k\Leftrightarrow\log_a\dfrac{b}{a^3b^2\sqrt{c}}=3-k\)
\(\Leftrightarrow\log_a\dfrac{1}{a^3.a^3.\sqrt{\dfrac{1}{a^2}}}=3-k\Leftrightarrow3-k=\log_a\dfrac{1}{a^5}\)
\(\Leftrightarrow\log_a\dfrac{1}{a}=\dfrac{3-k}{5}\Leftrightarrow\dfrac{1}{a}=a^{\dfrac{3-k}{5}}\Leftrightarrow-1=\dfrac{3-k}{5}\Leftrightarrow k=8\Rightarrow\log_ax=8\)
