Question

Sabendo que log 2 = 0,30 , log 3 = 0,47 e log 5 = 0,69 , calcule:

Log 6 na base 4

Answer 1

$log_{4}(6) = \frac{ log(6) }{ log(4) } = \frac{ log(2 \times 3) }{ log(2 \times 2) } = \\ = \frac{ log(2) + log(3) }{ log(2) + log(2) } = \frac{0.3 + 0.47}{0.3 + 0.3} = \\ = \frac{0.77}{0.6} = \frac{77}{60} = \boxed{1.28\overline3}$