Bài tập 2.48 trang 125 SBT Toán 12

Bài tập 2.48 trang 125 SBT Toán 12

a) ĐKXĐ: x > 0

Với x > 0, ta có: 

\(\begin{array}{l}
\log x + \log {x^2} = \log 9x\\
 \Leftrightarrow \log \left( {x.{x^2}} \right) = \log 9x\\
 \Leftrightarrow {x^3} = 9x\\
 \Leftrightarrow {x^2} = 9\\
 \Leftrightarrow x = 3
\end{array}\)

b) ĐKXĐ:  x > 0

Với x > 0, ta có: 

\(\begin{array}{l}
\log {x^4} + \log 4x = 2 + \log {x^3}\\
 \Leftrightarrow \log \left( {{x^4}.4x} \right) = \log \left( {100{x^3}} \right)\\
 \Leftrightarrow 4{x^5} = 100{x^3}\\
 \Leftrightarrow {x^2} = 25\\
 \Leftrightarrow x = 5
\end{array}\)

c) ĐKXĐ: \(x \in \left( { - \infty ; - 3} \right) \cup \left( {2; + \infty } \right)\) 

\(\begin{array}{l}
{\log _4}\left[ {\left( {x + 2} \right)\left( {x + 3} \right)} \right] + {\log _4}\frac{{x - 2}}{{x + 3}} = 2\\
 \Leftrightarrow {\log _4}\left[ {\left( {x + 2} \right)\left( {x + 3} \right).\frac{{x - 2}}{{x + 3}}} \right] = 2\\
 \Leftrightarrow {x^2} - 4 = {4^2}\\
 \Leftrightarrow {x^2} = 20\\
 \Leftrightarrow \left[ \begin{array}{l}
x = 2\sqrt 5 \\
x =  - 2\sqrt 5 
\end{array} \right.
\end{array}\)

d) ĐKXĐ: x > 2

\(\begin{array}{l}
{\log _{\sqrt 3 }}\left( {x - 2} \right){\log _5}x = 2{\log _3}\left( {x - 2} \right)\\
 \Leftrightarrow 2{\log _3}\left( {x - 2} \right){\log _5}x - 2{\log _3}\left( {x - 2} \right) = 0\\
 \Leftrightarrow {\log _3}\left( {x - 2} \right)\left( {{{\log }_5}x - 1} \right) = 0\\
 \Leftrightarrow \left[ \begin{array}{l}
{\log _3}\left( {x - 2} \right) = 0\\
{\log _5}x = 1
\end{array} \right.\\
 \Leftrightarrow \left[ \begin{array}{l}
x = 3\\
x = 5
\end{array} \right.
\end{array}\)

-- Mod Toán 12