Question

Sendo log2=0,30 e log3=0,47 determine:
a) S= log8 + log10
b) S= log√108 + log10
c) S= log 0,001 + log100

Answer 1

a) log 8 + log 10
 
log 8 = log 2³ = 3log2
log 10 = 1

3(0,30) + 1= 1,9


b) log √108 + log 10

fatorando 108:
2*2*3*3*3

log √108 = log 6√3 = log 6 + log √3 = log 2 + log 3 + 1/2 log 3 

0,30 + 0,47 + (0,47/2) + 1 = 2,005


c) log 0,001 + log 100

log 0,001 = log 10 / log 10 000 = log 10 / log 10^4 = log 10 - 4 log 10

log 100 = log 10² = 2 log 10

log 10 - 4 log 10 + 2 log 10

1 - 4 + 2 = -1
 
Espero ter ajudado!