Bài tập 38 trang 93 SGK Toán 12 NC

Bài tập 38 trang 93 SGK Toán 12 NC

a)

\(\begin{array}{l}
\log \frac{1}{8} + \frac{1}{2}\log 4 + 4\log \sqrt 2 \\
 =  - \log 8 + \log 2 + \log 4\\
 =  - \log 8 + \log 8 = 0
\end{array}\)

b)

\(\begin{array}{*{20}{l}}
\begin{array}{l}
\log \frac{4}{9} + \frac{1}{2}\log 36 + \frac{3}{2}\log \frac{9}{2}\\
 = \log \left( {\frac{4}{9}.6.\sqrt {{{\left( {\frac{9}{2}} \right)}^3}} } \right)\\
 = \log \left( {\frac{4}{9}.6.\frac{{{3^3}}}{2}.\sqrt {\frac{1}{2}} } \right)
\end{array}\\
{ = \log \left( {\frac{4}{9}{{.3}^4}.\frac{{\sqrt 2 }}{2}} \right) = \log \left( {18\sqrt 2 } \right)}
\end{array}\)

c)

\(\begin{array}{*{20}{l}}
\begin{array}{l}
\log 72 - 2\log \frac{{27}}{{256}} + \log \sqrt {108} \\
 = \log ({2^3}{.3^2}) - \log \frac{{{3^6}}}{{{2^{16}}}} + \log \sqrt {{2^2}{{.3}^3}} 
\end{array}\\
\begin{array}{l}
 = \log \left( {{2^3}{{.3}^2}:\frac{{{3^6}}}{{{2^{16}}}}{{.2.3}^{\frac{3}{2}}}} \right)\\
 = \log \left( {{2^{20}}{{.3}^{ - \frac{5}{2}}}} \right) = 20\log 2 - \frac{5}{2}\log 3
\end{array}
\end{array}\)

d)

\(\begin{array}{*{20}{l}}
\begin{array}{l}
\log \frac{1}{8} - \log 0,375 + 2\log \sqrt {0,5625} \\
 = \log {2^{ - 3}} - \log (0,{5^3}.3) + \log (0,{5^4}{.3^2})
\end{array}\\
\begin{array}{l}
 = \log {2^{ - 3}} - \log {2^{ - 3}} - \log 3 + 2\log {2^{ - 2}} + 2\log 3\\
 = \log {2^{ - 4}} + \log 3 = \log \frac{3}{{16}}
\end{array}
\end{array}\)

-- Mod Toán 12