1. Bila ³log 2 = p dan ²log 7 =q, nilai 14log 54 =…

(1. if ³log 2 = p and ²log 7 =q, value of 14log 54 =… )

Pembahasan (explaination) :

³log 2 = p   →   log 2 = p . log 3   … (1)

²log 7 = q   →   log 7 = q . log 2   … (2)

substitusi log 2 (1) ke (2) menjadi  :

(substitution of log 2 in (1) to (2) become : )

log 7 = q . log 2

= q . p . log 3

= pq . log 3

maka (then)  14log 54 = log 54 / log 14

= log (2 . 3³) / log (2 . 7)

= (log 2 + 3 . log 3) / (log 2 + log 7)

= (p . log 3 + 3 . log 3) / (p . log 3 + pq . log 3)

= log 3 (p + 3) / log 3 (p + pq)

= (p + 3) / (p + pq)

= (p + 3) / p(1 + q)

2. if 8log 5 = r, determine 5log 16 ?

explaination :

if 8log 5 = r  ↔  5log 8 = 1/r

5log 8 = 5log 2³ = 1/r

↔ 3.5log 2 = 1/r

↔ 5log 2 = 1/3r

then 5log 16 = 5log 2EXP4

= 4.5log 2

= 4.(1/3r)

= 4/3r

3. Jika 9log 8 = 3m, tentukan nilai 4log 3 ?

9log 8 = 3m  ↔  8log 9 = 1/3m

8log 9 = log 9 / log 8

1/3m = log 3² / log 2³

1/3m = 2.log 3 / 3.log 2

1/3m = 2/3 . 2log 3

2log 3 = 1/3m  :  2/3

= 1/3m  x  3/2

=  1/2m

4log 3 = log 3 / log 4

= log 3 / log 2²

= log 3 / 2.log 2

= ½ . 2log 3

= ½ . 1/2m

= 1/4m

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