Hãy tính
a) \({\log _{\sqrt 2 }}8\) b) \({\log _{\sqrt {{1 \over 3}} }}27\)
c) \({\log _{2\sqrt 2 }}128\) d) \({\log _{\sqrt 5 }}0,2\)
Giải
a) \({\log _{\sqrt 2 }}8 = {\log _{\sqrt 2 }}{\left( {\sqrt 2 } \right)^6} = 6\)
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b) \({\log _{\sqrt {{1 \over 3}} }}27 = {\log _{{3^{{{ - 1} \over 2}}}}}27 = - 2{\log _3}{3^3} = - 2.3 = - 6\)
c) \({\log _{2\sqrt 2 }}128 = {\log _{{{\left( {\sqrt 2 } \right)}^3}}}128 = {\log _{{2^{{3 \over 2}}}}}128\)
\(= {2 \over 3}{\log _2}{2^7} = {2 \over 3}.7 = {{14} \over 3}\)
d) \({\log _{\sqrt 5 }}0,2 = {\log _{{5^{{1 \over 2}}}}}{1 \over 5} = 2{\log _5}{5^{ - 1}} = 2.\left( { - 1} \right) = - 2\)