Question

CONSIDERANDO LOG2= 0,30 E LOG3= 0,47 CALCULE LOG6 NA BASE 4

Answer 1

Boa Noite!

use a P.M.B, propriedade de mudança de base:

$log_{b}(a) = \frac{ log_{c}(a) }{ log_{c}(b) }$

$log_{4}(6) = \frac{ log(6) }{ log(4) } \\ log_{4}(6) = \frac{ log(2 \times 3) }{ log(2^{2} ) } \\ log_{4}(6) = \frac{ log(2) + log(3) }{ log(2)^{2} }$

$log_{4}(6) = \frac{ log(2) + log(3) }{2 \times log(2) } \\ log_{4}(6) = \frac{0.3 + 0.47}{2 \times 0.3} \\ log_{4}(6) = \frac{0.77}{0.6}$

$log_{4}(6) = 1.283$

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