Question

Dados log2=0,30, log3=0,48 e log5=0,70 quanto vale
a)Log18
b)log45
c)log 250
d)log 1,25

Answer 1

$log\ 18 = log\ 2*3^2\\\\ log\ 18 = log\ 2+2\ log\ 3\\\\ log\ 18 = 0,3+2(0,48)\\\\ log\ 18 = 0,3+0,96\\\\ \boxed{log\ 18 = 1,26}$

$log\ 45 = log\ 3^2*5\\\\ log\ 45 = 2\ log\ 3+log\ 5\\\\ log\ 45 = 0,96+0,7\\\\ \boxed{log\ 45 = 1,66}$

$log\ 250 = log\ 10*5^2\\\\ log\ 250 = log\ 10+2\ log\ 5\\\\ log\ 250 = 1+1,4\\\\ \boxed{log\ 250=2,4}$

$log\ 1,25 = log\ \frac{5^3}{10^2}\\\\ log\ 1,25 = 3\ log\ 5-2\ log\ 10\\\\ log\ 1,25 = 2,1-2\\\\ \boxed{log\ 1,25=0,1}$

Answer 2

a) log 18  = 1,26

b) log 45  = 1,66

c) log 250  = 2,40

d) log 1,25 = 0,1

Explicação:

a) log 18  = log (2 x 3 x 3) =

log 2 + log 3 + log 3 = 0,30 + 0,48 + 0,48 = 1,26

b) log 45 = log (3 x 3 x 5) =

log 3 + log 3 + log 5 = 0,48 + 0,48 + 0,70 = 1,66

c) log 250 = log (2 x 5 x 5 x 5) =

log 2 + log 5 + log 5 + log 5 =  

0,30 + 0,70 + 0,70 + 0,70 = 2,40

d) log 1,25 = log (125/100) =

log 125 - log 100 =

log (5 x 5 x 5) - log (2 x 2 x 5 x 5) =

(log 5 + log 5 + log 5) - (log 2 + log 2 + log 5 + log 5) =

(0,70 + 0,70 + 0,70) - (0,30 + 0,30 + 0,70 + 0,70) =

(2,1) - (2) = 0,1

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