Question

1)$log_{ \frac{125}{27} }0,6$

2)$log_{0,0625} \frac{1}{1024}$

min ajudem com essa

Answer 1

Aplicando propriedades operatórias de logaritmos e de potencias

1)
             $log( \frac{125}{27} )0,6=x \\ \\ 0,6=( \frac{125}{27})^x \\ \\ \frac{6}{10} =( \frac{5^3}{3^3})^x \\ \\ \frac{3}{5} =( \frac{5}{3})^{3x} \\ \\ (\frac{5}{3}) ^{-1}= (\frac{5}{3} ) ^{3x} \\ \\ 3x=-1 \\ \\ x=- \frac{1}{3}$

2)
             $log(0,0625) \frac{1}{1024} =y \\ \\ \frac{1}{1024}=(0,0625)^y \\ \\ \frac{1}{ 2^{10} }= (\frac{625}{10000})^y \\ \\ ( \frac{1}{2}) ^{10} = (\frac{5^4}{10^4})^y \\ \\ ( \frac{5}{10}) ^{10} = ( \frac{5}{10}) ^{4y} \\ \\ 4y=10 \\ \\ y= \frac{10}{4} \\ \\ y= \frac{5}{2}$