giải pt sau: 1.2log(2x)=log(x^2+75) 2.(log5(5x))/(log5(x+1))=2 3.2log^2(x)-5log(x)+2=0 10/11/2021 Bởi Kennedy giải pt sau: 1.2log(2x)=log(x^2+75) 2.(log5(5x))/(log5(x+1))=2 3.2log^2(x)-5log(x)+2=0
Đáp án: 3) \(\left[ \begin{array}{l}x = 100\\x = \sqrt {10} \end{array} \right.\) Giải thích các bước giải: \(\begin{array}{l}1)DK:x > 0\\2\log 2x = \log \left( {{x^2} + 75} \right)\\ \to \log {\left( {2x} \right)^2} = \log \left( {{x^2} + 75} \right)\\ \to 4{x^2} = {x^2} + 75\\ \to 3{x^2} = 75\\ \to {x^2} = 25\\ \to \left[ \begin{array}{l}x = 5\left( {TM} \right)\\x = – 5\left( l \right)\end{array} \right.\\2)DK:x > 0\\\dfrac{{{{\log }_5}5x}}{{{{\log }_5}\left( {x + 1} \right)}} = 2\\ \to {\log _5}5x = 2{\log _5}\left( {x + 1} \right)\\ \to {\log _5}5x = {\log _5}{\left( {x + 1} \right)^2}\\ \to 5x = {x^2} + 2x + 1\\ \to {x^2} – 3x + 1 = 0\\ \to \left[ \begin{array}{l}x = \dfrac{{3 + \sqrt 5 }}{2}\\x = \dfrac{{3 – \sqrt 5 }}{2}\end{array} \right.\left( {TM} \right)\\3)DK:x > 0\\2{\log ^2}x – 5\log x + 2 = 0\\ \to \left[ \begin{array}{l}\log x = 2\\\log x = \dfrac{1}{2}\end{array} \right.\\ \to \left[ \begin{array}{l}x = 100\\x = \sqrt {10} \end{array} \right.\end{array}\) Bình luận
Đáp án:
3) \(\left[ \begin{array}{l}
x = 100\\
x = \sqrt {10}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
1)DK:x > 0\\
2\log 2x = \log \left( {{x^2} + 75} \right)\\
\to \log {\left( {2x} \right)^2} = \log \left( {{x^2} + 75} \right)\\
\to 4{x^2} = {x^2} + 75\\
\to 3{x^2} = 75\\
\to {x^2} = 25\\
\to \left[ \begin{array}{l}
x = 5\left( {TM} \right)\\
x = – 5\left( l \right)
\end{array} \right.\\
2)DK:x > 0\\
\dfrac{{{{\log }_5}5x}}{{{{\log }_5}\left( {x + 1} \right)}} = 2\\
\to {\log _5}5x = 2{\log _5}\left( {x + 1} \right)\\
\to {\log _5}5x = {\log _5}{\left( {x + 1} \right)^2}\\
\to 5x = {x^2} + 2x + 1\\
\to {x^2} – 3x + 1 = 0\\
\to \left[ \begin{array}{l}
x = \dfrac{{3 + \sqrt 5 }}{2}\\
x = \dfrac{{3 – \sqrt 5 }}{2}
\end{array} \right.\left( {TM} \right)\\
3)DK:x > 0\\
2{\log ^2}x – 5\log x + 2 = 0\\
\to \left[ \begin{array}{l}
\log x = 2\\
\log x = \dfrac{1}{2}
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 100\\
x = \sqrt {10}
\end{array} \right.
\end{array}\)
Đáp án:
Giải thích các bước giải: