Bài tập 2.16 trang 109 SBT Toán 12

Bài tập 2.16 trang 109 SBT Toán 12

a)

\(\begin{array}{l}
{\log _5}x = 2{\log _5}a - 3{\log _5}b \Leftrightarrow {\log _5}x = {\log _5}{a^2} - {\log _5}{b^3}\\
 \Leftrightarrow {\log _5}x = {\log _5}\frac{{{a^2}}}{{{b^3}}} \Leftrightarrow x = \frac{{{a^2}}}{{{b^3}}}
\end{array}\)

b)

\(\begin{array}{l}
lo{g_{\frac{1}{2}}}x = \frac{2}{3}lo{g_{\frac{1}{2}}}a - \frac{1}{5}lo{g_{\frac{1}{2}}}b \Leftrightarrow lo{g_{\frac{1}{2}}}x = lo{g_{\frac{1}{2}}}{a^{\frac{2}{3}}} - lo{g_{\frac{1}{2}}}{b^{\frac{1}{5}}}\\
 \Leftrightarrow lo{g_{\frac{1}{2}}}x = lo{g_{\frac{1}{2}}}\frac{{{a^{\frac{2}{3}}}}}{{{b^{\frac{1}{5}}}}}\\
 \Leftrightarrow x = \frac{{{a^{\frac{2}{3}}}}}{{{b^{\frac{1}{5}}}}} = \frac{{\sqrt[3]{{{a^2}}}}}{{\sqrt[5]{b}}}
\end{array}\)

-- Mod Toán 12