Question

dados log2= 0,301, log4=0,602, log5= 0,699 e log 6=0,778 calcule item a)log 120 item b) log 80 item c) log 40

Answer 1

$a) log(120) \\ 120| 2 \\ 60| 2 \\ 30|2 \\ 15| 3 \\ 5| 5 \\ 1| \\ \\ log( {2}^{3} \times 3 \times 5) \\ log( {2}^{3} ) + log(3) + log(5) \\ 3 log(2) + log( \frac{6}{2} ) + log(5) \\ 3 log(2) + ( log(6) - log(2) ) + log(5) \\ 3 \times 0.301 + (0.778 - 0.301) + 0.699 \\ 3 \times 0.301 + 0.477 + 0.699 \\ log(120) = 2.079 \\ \\ b) log(80) \\ 80| 2 \\ 40| 2 \\ 20| 2 \\ 10| 2 \\ 5| 5 \\ 1 \\ \\ log( {2}^{4 } \times 5) \\ log( {2}^{4} ) + log(5) \\ 4\times 0.301 + 0.699 \\ 1.216 + 0.699 \\ log(80) = 1.915 \\ \\ c) log(40) \\ log( {2}^{3} \times 5) \\ 3log(2) + log(5) \\ 3 \times 0.301 + 0.699 \\ log(40) = 1.602$