Trong mỗi trường hợp sau, hãy tính \({\log _a}x\) biết \({\log _a}b = 3,{\log _a}c = - 2\)
a) \(x = {a^3}{b^2}\sqrt c \)
b) \(x = \frac{{{a^4}\sqrt[3]{b}}}{{{c^3}}}\)
a)
\(\begin{array}{l}
{\log _a}x = {\log _a}\left( {{a^3}{b^2}\sqrt c } \right)\\
= 3 + 2{\log _a}b + \frac{1}{2}{\log _a}c\\
= 3 + 2.3 + \frac{1}{2}\left( { - 2} \right) = 8
\end{array}\)
b)
\(\begin{array}{l}
{\log _a}x = {\log _a}\left( {\frac{{{a^4}\sqrt[3]{b}}}{{{c^3}}}} \right)\\
= 4 + \frac{1}{3}{\log _a}b - 3{\log _a}c\\
= 4 + \frac{1}{3}.3 - 3\left( { - 2} \right) = 11
\end{array}\)
-- Mod Toán 12
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