Question

sabendo que log de 11 na base 6 é igual a 1,34 e log de 2 na base 6 é igual a 0,37, calcule

c) log 5,5 na base 6
e)log 11 na base 2
f) log 16 ba base 6

Answer 1

c)

$log_{6}(5,5)=log_{6}(55/10)\\log_{6}(5,5)=log_{6}(11/2)\\log_{6}(5,5)=log_{6}(11)-log_{6}(2)\\log_{6}(5,5)=1,34-0,37\\\\\boxed{\boxed{log_{6}(5,5)=0,97}}$

e)

$log_{2}(11)$

Mudando a base para 6:

$log_{2}(11)=\dfrac{log_{6}(11)}{log_{6}(2)}\\\\\\log_{2}(11)=\dfrac{1,34}{0,37}\\\\\\\boxed{\boxed{log_{2}(11)=3,62}}$

f)

$log_{6}(16)=log_{6}(2^{4})\\log_{6}(16)=4\cdot log_{6}(2)\\log_{6}(16)=4\cdot0,37\\\\\boxed{\boxed{log_{6}(16)=1,48}}$