a. ĐKXĐ: \(x>0\)
\(log_3x+log_3\left(x+2\right)=1\)
\(\Leftrightarrow log_3x\left(x+2\right)=1\)
\(\Leftrightarrow x\left(x+2\right)=3\)
\(\Leftrightarrow x^2+2x-3=0\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=-3\left(loại\right)\end{matrix}\right.\)
b.
ĐKXĐ: \(x\ge\sqrt{3}\)
\(log_2\left(x^2-3\right)-log_2\left(6x-10\right)+1=0\)
\(\Leftrightarrow log_2\left(\dfrac{x^2-3}{6x-10}\right)=-1\)
\(\Leftrightarrow\dfrac{x^2-3}{6x-10}=\dfrac{1}{2}\)
\(\Rightarrow2\left(x^2-3\right)-\left(6x-10\right)=0\)
\(\Leftrightarrow2x^2-6x+4=0\Rightarrow\left[{}\begin{matrix}x=1\left(loại\right)\\x=2\end{matrix}\right.\)
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