Question

Số nghiệm nguyên của bất phương trình:

\(2log_3\left(4x-3\right)+log_{\dfrac{1}{3}}\left(2x+3\right)\le2\)

Answer 1

ĐKXĐ: \(x\ge\dfrac{3}{4}\)

\(2log_3\left(4x-3\right)+log_{3^{-1}}\left(2x+3\right)\le2\)

\(\Leftrightarrow log_3\left(4x-3\right)^2-log_3\left(2x+3\right)\le2\)

\(\Leftrightarrow log_3\dfrac{\left(4x-3\right)^2}{2x+3}\le2\)

\(\Leftrightarrow\dfrac{\left(4x-3\right)^2}{2x+3}\le9\)

\(\Leftrightarrow\left(4x-3\right)^2\le9\left(2x+3\right)\)

\(\Leftrightarrow8x^2-21x-9\le0\)

\(\Rightarrow-\dfrac{3}{8}\le x\le3\)