Question

dados log10 2= 0,301 e log 10 3= 0,477 calcule:

log 10 raiz de 15?

Answer 1

Veja que, $\log_{10}\sqrt{15} = \log_{10}15^{\frac{1}{2}} = \dfrac{1}{2}\cdot\log_{10}15$
 
$\log_{10}15 = \log_{10}(3\cdot5) = \log_{10}3 + \log_{10}5$

Vamos calcular $\log_{10}5$.
 
$\log_{10}5=\log_{10}\dfrac{10}{2} = \log_{10}10-\log_{10}2=1-0,301=0,699$

Então: $\log_{10}15=0,477+0,699 = 1,176$

$\log_{10}\sqrt{15}=\dfrac{1}{2}\cdot1,176 = 0,588$