Question

Dado que log de 2 na base 14 = a e log de 3 na base 14 = b , calcule :a) log de 6 na base 14 b) log 7 na base 14 c) log de √1,5 na base 14 d) log de 3 na base 2 

Answer 1

De acordo com as propriedades logaritmicas:

a) $log_{14} 6=log_{14} (2.3)=log_{14} 2+log_{14} 3=a+b$


b) $log_{14} 7=log_{14} \frac{14}{2} =log_{14}14-log_{14} 2=1-a$


c) $log_{14} \sqrt{1,5}=log_{14} \sqrt{ \frac{3}{2} } =log_{14} ( \frac{3}{2})^\frac{1}{2}= \frac{1}{2} .log_{14} \frac{3}{2} = \frac{1}{2} (log_{14} 3-log_{14} 2) \\ = \frac{1}{2}(b-a)$


d) $log_{2} 3= \frac{log_{14} 3}{log_{14} 2} = \frac{b}{a}$