Question

Bài 2: Giải pt, bpt sau:

7) \(\dfrac{2.3^x - 2^{x+2}}{3^x-2^x} ≤ 1\)

Answer 1

\(\Leftrightarrow\dfrac{2.3^x-2^x.4}{3^x-2^x}-1\le0\Leftrightarrow\dfrac{2.3^x-2^x.4-3^x+2^x}{3^x-2^x}\le0\)

\(\Leftrightarrow\dfrac{3^x-3.2^x}{3^x-2^x}\le0\Leftrightarrow\dfrac{1-3.\left(\dfrac{2}{3}\right)^x}{1-\left(\dfrac{2}{3}\right)^x}\le0\)

TH1 : \(\left\{{}\begin{matrix}x\ge log_{\dfrac{2}{3}}^{\dfrac{1}{3}}\\x\le0\end{matrix}\right.\left(l\right)\)

TH2 : \(0\le x\le log_{\dfrac{2}{3}}^{\dfrac{1}{3}}\)