Question

Log 0,6 na base 125/27
Me ajudem!!!

Answer 1

$\mathrm{\ell og}_{\frac{125}{27}\,}0,6=x\;\;\Rightarrow\;\;\left(\dfrac{125}{27} \right )^{x}=0,6\\ \\ \\ \left(\dfrac{5^{3}}{3^{3}} \right )^{x}=\dfrac{3}{5}\\ \\ \\ \left[\left(\dfrac{5}{3} \right )^{3} \right ]^{x}=\left(\dfrac{5}{3} \right )^{-1}\\ \\ \\ \left(\dfrac{5}{3} \right )^{3x}=\left(\dfrac{5}{3} \right )^{-1}\\ \\ \\ 3x=-1\\ \\ x=-\dfrac{1}{3}\;\;\Rightarrow\;\;\boxed{ \begin{array}{c} \mathrm{\ell og}_{\frac{125}{27}\,}0,6=-\dfrac{1}{3} \end{array} }$