Question

Sendo log 2 = 0,3; log3 = 0,4 e log5 = 0,7, calcule:

a) log 50 na base 2 b) log 45 na base 3

c) log 2 na base 9 d) log 600 na base 8

f) log 15 na base 6

Answer 1

a) Log₂(50)

Log₂5 + Log₂5 + Log₂2

Log(5)/Log(2) + Log(5)/Log(2) + 1

( 0,7/0,3 ) * 2 + 1

14/3 + 1

17/3

b) Log₃45

Log₃3 + Log₃3 + Log₃5

1 + 1 + Log5/Log3

2 + 0,7/0,4

(7 + 8)/4

15/4

c) Log₂9

Log₂3 + Log₂3

Log3/Log2 + Loq3/Log2

2(0.4/0.3)

8/3

d) Log₈600

(2Log5 + 3Log2 + Log3)/3Log2

(1.4 + 0.9 + 0.4)/0.9

(2.7)/0.9 = 3

e) ou "f)"

(Log5 + Log3)/(Log2 + Log3)

(0.7 + 0.4)/(0.3 + 0.4)

1.1/0.7 = 11/7