Cho \({\log _{\frac{1}{2}}}x = \frac{2}{3}{\log _{\frac{1}{2}}}a - \frac{1}{5}{\log _{\frac{1}{2}}}b\). Tìm x

Hàm số mũ | Hàm số lũy thừa | Hàm số mũ và lũy thừa | hàm số loagrit | logarit |
Cho \({\log _{\frac{1}{2}}}x = \frac{2}{3}{\log _{\frac{1}{2}}}a - \frac{1}{5}{\log _{\frac{1}{2}}}b\). Tìm x.
A. \({a^{\frac{3}{2}}}.{b^{\frac{1}{5}}}\)
B. \(\frac{{{a^{\frac{3}{2}}}}}{{{b^{\frac{1}{5}}}}}\)
C. \(\frac{{{a^{\frac{2}{3}}}}}{{{b^{\frac{1}{5}}}}}\)
D. \(\frac{{{a^{\frac{3}{2}}}}}{{{b^5}}}\)

\(\begin{array}{l}{\log _{\frac{1}{2}}}x = \frac{2}{3}{\log _{\frac{1}{2}}}a - \frac{1}{5}{\log _{\frac{1}{2}}}b \Leftrightarrow {\log _{\frac{1}{2}}}x = {\log _{\frac{1}{2}}}{a^{\frac{2}{3}}} - {\log _{\frac{1}{2}}}{b^{\frac{1}{5}}}\\ \Leftrightarrow {\log _{\frac{1}{2}}}x = {\log _{\frac{1}{2}}}\frac{{{a^{\frac{2}{3}}}}}{{{b^{\frac{1}{5}}}}} \Leftrightarrow x = \frac{{{a^{\frac{2}{3}}}}}{{{b^{\frac{1}{5}}}}}\end{array}\)