Đáp án:
3) \(\left[ \begin{array}{l}
x = 100\\
x = \sqrt {10}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
1)DK:x > 0\\
2\log 2x = \log \left( {{x^2} + 75} \right)\\
\to \log {\left( {2x} \right)^2} = \log \left( {{x^2} + 75} \right)\\
\to 4{x^2} = {x^2} + 75\\
\to 3{x^2} = 75\\
\to {x^2} = 25\\
\to \left[ \begin{array}{l}
x = 5\left( {TM} \right)\\
x = - 5\left( l \right)
\end{array} \right.\\
2)DK:x > 0\\
\dfrac{{{{\log }_5}5x}}{{{{\log }_5}\left( {x + 1} \right)}} = 2\\
\to {\log _5}5x = 2{\log _5}\left( {x + 1} \right)\\
\to {\log _5}5x = {\log _5}{\left( {x + 1} \right)^2}\\
\to 5x = {x^2} + 2x + 1\\
\to {x^2} - 3x + 1 = 0\\
\to \left[ \begin{array}{l}
x = \dfrac{{3 + \sqrt 5 }}{2}\\
x = \dfrac{{3 - \sqrt 5 }}{2}
\end{array} \right.\left( {TM} \right)\\
3)DK:x > 0\\
2{\log ^2}x - 5\log x + 2 = 0\\
\to \left[ \begin{array}{l}
\log x = 2\\
\log x = \dfrac{1}{2}
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 100\\
x = \sqrt {10}
\end{array} \right.
\end{array}\)
