Page 30 - X_Matematika-Peminatan_KD-3.1_Final_Neat

Modul Matematika Peminatan Kelas X KD 3.1

Contoh 1.
Sederhanakan bentuk logaritma berikut:

a. 2 log 8 + log 4
2
1
1
1

b. log × log × log

1
1
3
3
3
3
c. log 24 − log 2√3 + 2. log + log 2
9 4
Jawab
a. 2 log 8 + log 4 = log (8  4)
2
2
= log 32
2
= log 2
2
5
= 5. log 2
2
= 5.1
= 5
1
1
1

b. log × log × log = log −1 × log −1 × log −1

= (− log ) × (− log ) × (− log )

= − log × log × log

= − log

= −1
1
1
c. log 24 − log 2√3 + 2. log + log 2
3
3
3
3
9 4
1 2 9
3
3
3
= log 24 − log 2√3 + log ( ) + log
3
9 4
1 9
24 × ×
3
= log 81 4
2√3
2
3
= log 3
2√3
1 1
3
3
= log = log 3
3√3 3 2
3 3
−
3
= log 3 2 = −
2

Contoh 2.
3
5
Diketahui log 3 = dan log 4 = , tentukan 12 log 75 dalam a dan b.
Jawab
3
3
log 75 log(3 × 25)
12 log 75 = =
3
3
log 12 log(3 × 4)
3
3
3
3
log 3 + log 25 log 3 + log 5 2
= =
3
3
3
3
log 3 + log 4 log 3 + log 4
3
1 +2. log 5
=
3
1 + log 4
1
1 + 2 × + 2
= =
1 + (1 + )

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