Diketahui : ²log3 = p dan ²log5 = q
Tentukan = ²log18 ?,²log10?,²log75?,²log90?
Jawab??!![]()
Tentukan = ²log18 ?,²log10?,²log75?,²log90?
Jawab??!
Sifat Logaritma yang digunakan:
[tex]{}^{a} \log {b} + {}^{a} \log {c} = {}^{a} \log {(b \times c)} [/tex]
[tex]{}^{a^{n}} \log {b^{m}} = \frac{m}{n} . {}^{a} \log {b}\\[/tex]
[tex]{}^{a} \log {a} = 1[/tex]
[tex]\\[/tex]
Diketahui:
²log 3 = p
²log 5 = q
[tex]\\[/tex]
²log 18
= ²log (9 × 2)
= ²log 9 + ²log 2
= ²log 3² + ²log 2
= 2. ²log 3 + ²log 2
= 2p + 1
[tex]\\[/tex]
²log 10
= ²log (5 × 2)
= ²log 5 + ²log 2
= q + 1
[tex]\\[/tex]
²log 75
= ²log (25 × 3)
= ²log 25 + ²log 3
= ²log 5² + ²log 3
= 2. ²log 5 + ²log 3
= 2q + p
[tex]\\[/tex]
²log 90
= ²log (9 × 5 × 2)
= ²log 9 + ²log 5 + ²log 2
= ²log 3² + ²log 5 + ²log 2
= 2. ²log 3 + ²log 5 + ²log 2
= 2p + q + 1
[tex]\\[/tex]
Semoga membantu.
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