Question

Passe os logaritmos abaixo para base 3:



a)Log 27
9

b)Log 12
2

Answer 1

Olá, tudo bem?

$\text{a)}\,\,\log_{9}27=\log_{(3^2)}(3^3)=3\cdot\dfrac{1}{2}\cdot \log_{3}(3)=\dfrac{3}{2},\quad\text{pois}\,\,\log_{3}(3)=1$

$\text{b)}\,\,\log_{2}(12)\underrightarrow{\quad\text{base 3}\quad}\,\,\dfrac{\log_{3}(12)}{\log_{3}(2)}=\\\\\\=\dfrac{\log_{3}(2^2)+\log_{3}(3)}{\log_{3}(2)}=\\\\\\=\dfrac{2\cdot\log_{3}(2)+1}{\log_{3}(2)}=\\\\\\=2+\dfrac{1}{\log_{3}(2)}$

É isso!! :)