Question

alguem pode me ajudar ?
log4/9 na base 1,5

Answer 1

$\log_{1{,}5}\left(\dfrac{4}{9}\right)=x\ \Leftrightarrow\ 1{,}5^x=\dfrac{4}{9}\\\\\\\left(\dfrac{15}{10}\right)^x=\dfrac{4}{9}\\\\\\\left(\dfrac{3}{2}\right)^x=\dfrac{4}{9}\\\\\\\left(\dfrac{3}{2}\right)^x=\left(\dfrac{2}{3}\right)^2\\\\\\\left(\dfrac{3}{2}\right)^x=\left(\dfrac{3}{2}\right)^{-2}\ \ \therefore\ \ x=-2\\\\\\\\\boxed{S=\{-2\}}$