5 log 30 atau 8 log 60? Manakah nilai terbesar

Anggap 2'log 3 = a dan 2'log 5 = b

5'log 30 = 2'log 30 ÷ 2'log 5
= 2'log (2 × 3 × 5) ÷ 2'log 5
= (1 + 2'log 3 + 2'log 5) ÷ 2'log 5
= (1 + a + b) ÷ b

8'log 60 = 2^3'log (2 × 2 × 3 × 5)
= (1/3) × (2'log 2 + 2'log 2 + 2'log 3+ 2'log 5)
= (1/3) × (2 + 2'log 3 + 2'log 5)
= (1/3) × (2 + a + b)


Maka didapatkan
(1 + a + b)/b dan (2 + a + b)/3

Hasilnya,
[(1 + a + b)/b] > [(2 + a + b)/3]
Jadi 5'log 30 > 8'log 60