Question

Log 0,2 ³√25


Log 0,01



Log 1,25 0,64



Log 5/3 0,6

Answer 1

oK!

Definição de logaritmo

$log^{b}_{a} =x\ \textless \ -\ \textgreater \ a ^{x} = b$

Resolvendo

$log _{0,2} ^{ \sqrt[3]{25} } \\ \\ 0,2 ^{x} = \sqrt[3]{25} \\ \\ (\dfrac{2}{10}) ^{x} =25 ^{ \frac{1}{3} } \\ \\ \\ (\dfrac{1}{5})^{x}= (5 ^{2}) ^{ \frac{1}{3} } \\ \\ \\ 5 ^{-x} =5 ^{ \frac{2}{3} } \\ \\ \\ -x=\dfrac{2}{3} \\ \\ \\ x=-\dfrac{2}{3}$

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$log0,01 \\ \\ 10 ^{x} =0,01 \\ \\ 10 ^{x}= \dfrac{1}{100} \\ \\ 10 ^{x}=10 ^{-2} \\ \\ x=-2$
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$log _{1,25} ^{0,64} \\ \\ \\ 1,25 ^{x} =0,64 \\ \\ \\ ( \dfrac{125}{100}) ^{x}= \dfrac{64}{100} \\ \\ \\ (\dfrac{5}{4} ) ^{x}= \dfrac{16 }{25} \\ \\ \\ (\dfrac{5}{4} ) ^{x}= (\dfrac{4}{5})^{2} \\ \\ \\ (\dfrac{5}{4} ) ^{x}= (\dfrac{5}{4} ) ^{-2 } \\ \\ x=-2$

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$log _{ \frac{5}{3} } ^{0,6} \\ \\ (\dfrac{5}{3} ) ^{x} =0,6 \\ \\ \\ (\dfrac{5}{3} ) ^{x}= \dfrac{6}{10} \\ \\ \\ (\dfrac{5}{3} ) ^{x}= \dfrac{3}{5} \\ \\ \\ (\dfrac{5}{3} ) ^{x}= (\dfrac{5}{3}) ^{-1} \\ \\ x=-1$