Bài 2.12: Tính:
a) \({(\frac{1}{9})^{\frac{1}{2}{{\log }_3}4}}\)
b) \({10^{3 – \log 5}}\)
c) \(2{\log _{27}}\log 1000\)
d) \(3{\log _2}{\log _4}16 + {\log _{\frac{1}{2}}}2\)
a) \(\frac{1}{4}\)
b) \(\frac{{{{10}^3}}}{{{{10}^{\log 5}}}} = \frac{{{{10}^3}}}{5} = 200\)
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c) \(\frac{2}{3}\)
d) 2
Bài 2.13: Tính:
a) \(\frac{1}{2}{\log _7}36 – {\log _7}14 – 3{\log _7}\sqrt[3]{{21}}\)
b) \(\frac{{{{\log }_2}24 – \frac{1}{2}{{\log }_2}72}}{{{{\log }_3}18 – \frac{1}{3}{{\log }_3}72}}\)
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c) \(\frac{{{{\log }_2}4 + {{\log }_2}10}}{{{{\log }_2}20 + 3{{\log }_2}2}}\)
a) \({\log _7}\sqrt {36} – {\log _7}14 – {\log _7}21 = {\log _7}\frac{1}{{49}} = – 2\)
b) \(\frac{{{{\log }_2}24 – {{\log }_2}\sqrt {72} }}{{{{\log }_3}18 – {{\log }_3}\sqrt[3]{{72}}}} = \frac{{{{\log }_2}{2^{\frac{3}{2}}}}}{{{{\log }_3}{3^{\frac{4}{3}}}}} = \frac{9}{8}\)
c) \(\frac{{{{\log }_2}24 – {{\log }_2}\sqrt {72} }}{{{{\log }_3}18 – {{\log }_3}\sqrt[3]{{72}}}} = \frac{{{{\log }_2}{2^{\frac{3}{2}}}}}{{{{\log }_3}{3^{\frac{4}{3}}}}} = \frac{9}{8}\).
Bài 2.14: Tìm x, biết:
a) \({\log _5}x = 2{\log _5}a – 3{\log _5}b\)
b) \({\log _{\frac{1}{2}}}x = \frac{2}{3}{\log _{\frac{1}{2}}}a – \frac{1}{5}{\log _{\frac{1}{2}}}b\)
a) \(x = \frac{{{a^2}}}{{{b^3}}}\)
b) \(x = \frac{{{a^{\frac{2}{3}}}}}{{{b^{\frac{1}{5}}}}}\).
