Question

Jika diketahui log 3 = 0,4771 dan log 5 = 0,6990, tentukan :
a. Log 45
b. Log 25
c. Log 0,36
d. Log 135
e. Log 5/3
f. Log √135

Answer 1

A)
= log 45
= log (3 x 3 x 5)
= log 3 + log 3 + log 5
= 0,4771 + 0,4771 + 0,6990
= 1,6532

b)
= log 25
= log (5 x 5)
= log 5 + log 5
= 0,6990 + 0,6990
= 1,3980

c)
= log 0,36
= log (9 : 25) 
= log 9 - log 25
= log 3²  -  log 5²
= 2 x log 3  - 2 x log 5
= 2 x (log 3 - log 5)
= 2 x (0,4771 - 0,6990)
= 2 x ( - 0,2219 )
= - 0,4438

d)
= log 135
= log (27 x 5)
= log 27 + log 5
= log 3³ + log 5
= 3 x log 3 + log 5
= 3 x 0,4771 + 0,6990
= 2,1303
 
e)
= log 5/3
= log 5 - log 3
= 0,6990 - 0,4771
= 0,2219

f)
= log √135
= 1/2 x log 135
= 1/2 x log (27 x 5)
= 1/2 x [ log 27 + log 5 ]
= 1/2 x [ log 3³ + log 5 ]
= 1/2 x [ 3 x log 3 + log 5 ]
= 1/2 x [ 3 x 0,4771 + 0,6990 ]
= 1/2 x [ 2,1303]
= 1,06515