Question

Jika 2log 5 = P, nyatakan logaritma berikut dalam P
A. 3 log 50
B. 20 log 160
C. 2 log 20
D. 5 log 40

Answer 1

Nomor A.
3 log 50 = 3 log (100/2)
= 3[ log 100 - log 2]
= 3[ log 100 - log 10/5]
= 3[ log 100 - (log 10 - log 5)]
= 3 log 100 - 3(log 10 - log 5)]
= 3 log 100 - 3 log10 - 3log 5
= 3(2) - 3(1) - P
= 6 -3 - P
= 3 - P

Jadi,
3 log 50 = 3 - P


Nomor B.
20 log 160 = 20 log {10 × [100/(5^2)]^2}
=20 log 10 + 20 log [100/(5^2)]^2
=20 log 10 + 40 log [100/(5^2)]
=20 log 10 + 40 log 100 - 40 log 5^2
=20 log 10 + 40 log 100 - 80 log 5

Karena 2log5 = P ⇔ log 5 = P/2

sehingga 20 log 160
= 20(1)+ 40(2) - 80(P/2)
= 20 + 80 - 40P
= 100 - 40P


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