Jika 6log 8=p maka 9log 6

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jika 6log 8=p maka 9log 6

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1 jika 6log 8=p maka 9log 6
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Jawaban : 3/(6-2p)

Penyelesaian :
Konsep :
a^n log b^m = m/n . alogb
a^n log b = 1/n alogb
alog b^m = m. alogb
alogb = 1/bloga

Sehingga
⁶log 8=p
⁶log 2³ = p
3.⁶log2 = p
⁶log 2 = p/3
²log 6 = 3/p
²log (2×3) = 3/p
²log2 + ²log 3 = 3/p
1+²log3 = 3/p
²log 3 = 3/p – 1
²log 3 = (3-p)/p
³log 2 = p / (3-p)

Maka
⁹log 6 = 3^2 log 6
= 1/2 ³log6
= 1/2 ( ³log(3×2))
= 1/2 ( ³log3 + ³log2 )
= 1/2 ( 1 + p/(3-p) )
= 1/2 ( (3-p)+p )/(3-p)
= 1/2 ( 3/(3-p))
= 3/(2(3-p))
= 3/(6-2p)

Kesimpulan , jika 6log 8=p maka 9log 6 adalah 3/(6-2p)

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