Question

sendo log.2=0,30; log.3=0,48 e log. 4=0,70 calcule o valor de log .16 e log.50

Answer 1

Olá!

log 2 = 0,30
log 3 = 0,48
log 4 = 0,70

1) log 16
$= log (16) \\ = log (2^4)$
Propriedade:
$\boxed{log_b(a^x) = x \times log_b(a) }$
$= 4 \times log (2) \\ = 4 \times 0,30 \\ \boxed{= 1,2}$

2)
$= log (50) \\ = log (2 \times 5^2) \\ = log (2) + log (5^2) \\ = 0,30 + ( 2 \times log (5) ) \\ = 0,30 + ( 2 \times log (\frac{10}{2}) ) \\ = 0,30 + [ 2 \times ( log (10) - log (2) )] \\ = 0,30 + [2 \times ( 1 - 0,30)] \\ = 0,30 + [ 2 \times 0,7] \\ = 0,30 + 1,4 \\ \boxed{= 1,7}$

Notas:
$\boxed{ log (a) = log_{10}(a)}$
log 1 = 0
log 10 = 1
log 100 = 2
log 1.000 = 3
...

Bons estudos.