Question

Se log 2 = a, log 3 = b e log 5 = c, então calcule os logaritmos abaixo em função de a, b е с.
a) log 40
b) log 48
c) log 135
d) log 1536
e) log 30
o log 540​

Answer 1

a) Log 40

= Log 2³ * 5

= Log 2³ + Log 5

= 3 Log 2 + Log 5

= 3 * a + c

= 3a + c

b) Log 48

= Log 2⁴ * 3

= Log 2⁴ + Log 3

= 4 Log 2 + Log 3

= 4 * a + b

= 4a + b

c) Log 135

= Log 3³ * 5

= Log 3³ + Log 5

= 3 Log 3 + Log 5

= 3 * b + c

= 3b + c

d) Log 1536

= Log 2⁹ * 3

= Log 2⁹ + Log 3

= 9 Log 2 + Log 3

= 9 * a + b

= 9a + b

e) Log 30

= Log 2 * 3 * 5

= Log 2 + Log 3 + Log 5

= a + b + c

f) Log 540

= Log 2² * 3³ * 5

= Log 2² + Log 3³ + Log 5

= 2 Log 2 + 3 Log 3 + Log 5

= 2 * a + 3 * b + c

= 2a + 3b + c