Question

Sendo Log 2 = 0,3; Log3 = 0,4 e Log = 0,7, Calcule.

Log3 Base 45

Answer 1

$\log_{45} 3$

Mudando para base 10, teremos:

$\log_{45} 3= \dfrac{\log 3}{\log 45} = \dfrac{0,4}{\log 9\cdot 5} =\dfrac{0,4}{\log 9 + \log 5}=\dfrac{0,4}{\log 3^{2} + 0,7}=\\ \\ \\ \dfrac{0,4}{2\log 3 + 0,7}=\dfrac{0,4}{2\cdot 0,4 + 0,7}=\dfrac{0,4}{0,8 + 0,7}=\dfrac{0,4}{1,5}=0,2666...$


Ou:

$\dfrac{0,4}{1,5}=\dfrac{\dfrac{4}{10}}{\dfrac{15}{10}}=\dfrac{4}{\not 10}\cdot \dfrac{\not 10}{15}=\dfrac{4}{15}=0,2666...$