Giải Bài 5 trang 19 SGK Toán 11 Chân trời sáng tạo tập 2 - CTST

Lời giải chi tiết

a) \({\log _2}9.{\log _3}4 \)\(= {\log _2}{3^2}.{\log _3}4 \)\(= 2{\log _2}3.{\log _3}4 \)\(= 2{\log _2}4 \)\(= 2{\log _2}{2^2} \)\(= 2.2 = 4\).

b) \({\log _{25}}\frac{1}{{\sqrt 5 }}\)\( = {\log _{{5^2}}}{5^{ - \frac{1}{2}}} \)\(= \frac{{ - \frac{1}{2}}}{2}{\log _5}5 \)\(= - \frac{1}{4}\).

c)

\(\begin{array}{*{20}{l}}
\begin{array}{l}
{\log _2}3.{\log _9}\sqrt 5 .{\log _5}4\\
 = {\log _2}3.{\log _{{3^2}}}{5^{\frac{1}{2}}}.{\log _5}{2^2}\\
 = {\log _2}3.\frac{{\frac{1}{2}}}{2}{\log _3}5.2{\log _5}2
\end{array}\\
\begin{array}{l}
 = \frac{1}{2}{\log _2}3.{\log _3}5.{\log _5}4\\
 = \frac{1}{2}{\log _2}5.{\log _5}2\\
 = \frac{1}{2}{\log _2}2 = \frac{1}{2}
\end{array}
\end{array}\)

-- Mod Toán 11 HỌC247