Question

Dados  log 2 = 0,30 e log 3 = 0,48 DETERMINE :


a-  log 3 na base 2 

b-   log 32 na base 9 

c-   log raiz de 3

Answer 1

Temos que fazer mudança de base:

a) $log_{2}3 = \frac{log_{10}3}{log_{10}2} = \frac{0,30}{0,48} = \boxed{\boxed{0,625}}$


b) $log_{9}32 = \frac{log32}{log9} = \frac{log2^{5}}{log3^{2}} = \frac{5 \cdot log2}{2 \cdot log3} = \frac{5 \cdot 0,3}{2 \cdot 0,48} = \frac{1,5}{0,96} = \boxed{\boxed{1,5625}}$


c) $log\sqrt{3} = log3^{\frac{1}{2}} = \frac{1}{2} \cdot 0,48 = \boxed{\boxed{0,24}}$