Question

Sendo Log 2= 0,3 , Log 3= 0,4 , Log 5=0,7 e Log 7 =

A) Log 120
B) Log 90
C)Log 75
D) Log 45
E) Log 180
F)Log 100
G) Log 42
H)Log 48​

Answer 1

Explicação passo-a-passo:

Para isso, simplificamos cada Log em fatores primos:

A) Log 120  

$120 = 2^{3} * 3*5\\\\Log 120 = Log 2^{3} + Log 3 + Log 5\\Log 120=3*Log 2 + Log 3 + Log 5\\Log 120=3*(0,3)+0,4+0,7\\Log 120 = 2$

B) Log 90

$90 = 3^{2} *2*5\\\\Log 90 = Log3^{2} + Log 2 + Log 5\\Log 90 = 2*Log3 + Log 2 + Log 5\\Log90 = 2*0,4 + 0,3 + 0,7\\Log 90 = 1,8$

C)Log 75

$75 = 5^{2} *3\\\\Log 75 = Log5^{2} + Log 3\\Log 75 = 2*Log5 + Log 3\\Log 75 = 2*0,7 + 0,4\\Log 75 = 1,8$

D) Log 45

$45 = 3^{2}*5\\\\Log 45 = Log3^{2} + Log 5\\Log 45 = 2*Log3 + Log 5\\Log45 = 2*0,4 + 0,7\\Log 45 = 1,5$

E) Log 180

$180 = 3^{2} *2^{2}*5\\\\Log 180 = Log3^{2} + Log 2^{2} + Log 5\\Log 180 = 2*Log3 + 2*Log 2 + Log 5\\Log180 = 2*0,4 + 2*0,3 + 0,7\\Log 180 = 2,1$

F) Log 100

$100 = 2^{2}*5^{2}\\\\Log 100 = Log2^{2} + Log 5^{2}\\Log 100 = 2*Log2 + 2*Log 5\\Log100 = 2*0,3 + 2*0,7\\Log 100 = 2$

G) Log 42

$42 = 3*2*7\\\\Log 42 = Log3 + Log 2 + Log 7\\Log 42 = Log3 + Log 2 + Log 7\\Log42 = 0,4 + 0,3 + 0,8\\Log 42 = 1,5$

H) Log 48

$48 = 2^{4}*3\\\\Log 48 = Log2^{4} + Log 3\\Log 48 = 4*Log2 + Log 3\\Log48 = 4*0,3 + 0,4\\Log 48 = 1,6$