- LG a
- LG b
- LG c
- LG d
Đơn giản các biểu thức:
LG a
\[\log {1 \over 8} + {1 \over 2}\log 4 + 4\log \sqrt 2 \]
Lời giải chi tiết:
\[\log {1 \over 8} + {1 \over 2}\log 4 + 4\log \sqrt 2 \]
\[\begin{array}{l}
= \log \frac{1}{8} + \log {4^{\frac{1}{2}}} + \log {\left[ {\sqrt 2 } \right]^4}\\
= \log \frac{1}{8} + \log \sqrt 4 + \log {\left[ {{{\left[ {\sqrt 2 } \right]}^2}} \right]^2}\\= \log \frac{1}{8} + \log 2 + \log 4\\
= \log \left[ {\frac{1}{8}.2.4} \right]\\
= \log 1\\
= 0
\end{array}\]
LG b
\[\log {4 \over 9} + {1 \over 2}\log 36 + {3 \over 2}\log {9 \over 2}\]
Lời giải chi tiết:
\[\log {4 \over 9} + {1 \over 2}\log 36 + {3 \over 2}\log {9 \over 2}\]
\[\begin{array}{l}
= \log \frac{4}{9} + \log {36^{\frac{1}{2}}} + \log {\left[ {\frac{9}{2}} \right]^{\frac{3}{2}}}\\
= \log \frac{4}{9} + \log 6 + \log \left[ {\sqrt {{{\left[ {\frac{9}{2}} \right]}^3}} } \right]\\
= \log \left[ {\frac{4}{9}.6.\sqrt {{{\left[ {\frac{9}{2}} \right]}^3}} } \right]\\
= \log \left[ {\frac{8}{3}.\frac{9}{2}\sqrt {\frac{9}{2}} } \right]\\
= \log \left[ {12.\frac{3}{{\sqrt 2 }}} \right]\\
= \log \left[ {18\sqrt 2 } \right]
\end{array}\]
LG c
\[\log 72 - 2\log {{27} \over {256}} + \log \sqrt {108} \]
Lời giải chi tiết:
LG d
\[\log {1 \over 8} - \log 0,375 + 2\log \sqrt {0,5625} \]
Lời giải chi tiết:
\[\begin{array}{l}
= \log \frac{1}{8} - \log \frac{3}{8} + \log {\left[ {\sqrt {0,5625} } \right]^2}\\
= \log \frac{1}{8} - \log \frac{3}{8} + \log 0,5625\\
= \log \frac{1}{8} - \log \frac{3}{8} + \log \frac{9}{{16}}\\
= \left[ {\log \frac{1}{8} + \log \frac{9}{{16}}} \right] - \log \frac{3}{8}\\
= \log \left[ {\frac{1}{8}.\frac{9}{{16}}} \right] - \log \frac{3}{8}\\
= \log \frac{9}{{128}} - \log \frac{3}{8}\\
= \log \left[ {\frac{9}{{128}}:\frac{3}{8}} \right]\\
= \log \frac{3}{{16}}
\end{array}\]