Question

Sendo lig2=9,30, Log3=0,48 e Log7= 0,85, determine :
Log 196
E log 72

Answer 1

$log(196)$

mmc de 196
196|2
 98 |2
49 | 7
7 | 7 
1 
196 = 2*2*7*7 = 2²*7²
$log(196)\\\\=log(2^2*7^2)\\\\=log(2^2)+log(7^2)\\\\=2*log(2)+2*log(7)\\\\=2*0,30 + 2*0,85 = 2,3$



log(72)

mmc ..72
72| 2
36|2
18 | 2
9 | 3
3 | 3
1
72= 2³ * 3²

$log(72)\\\\=log(2^3*3^2)\\\\=log(2^3)+log(3^2)\\\\=3*log(2)+2*log(3)\\\\=3*0,30+2*0,48=1,86$