Question

Tolong dibantu ya Diketahui 120 log 3 = a dan 120 log 2 = b. berapa nilai dari 3 log 25 + 5 log 4 =...

Answer 1

Kategori Soal : Matematika - Logaritma
Kelas : X (1 SMA)
Pembahasan :
Diketahui 
¹²⁰log 3 = a 
⇔ log 3/log 120 = a
⇔ log 3 = a x log 120
⇔ log 3 = a x log (3 x 4 x 10)
⇔ log 3 = a x (log 3 + log 4 + log 10)
⇔ log 3 = a x log 3 + a x log 4 + a x log 10
⇔ log 3 = a x log 3 + a x log 2² + a x 1
⇔ log 3 = a x log 3 + 2a x log 2 + a
⇔ ⁵log 3 = a x ⁵log 3 + 2a x ⁵log 2 + a
⇔ ³log 5 = 1/(a x ⁵log 3 + 2a x ⁵log 2 + a)

¹²⁰log 2 = b
⇔ log 2/log 120 = b
⇔ log 2 = b x log 120
⇔ log 2 = b x (log 3 x 4 x 10)
⇔ log 2 = b x (log 3 + log 4 + log 10)
⇔ log 2 = b x log 3 + b x log 4 + b x log 10
⇔ log 2 = b x log 3 + b x log 2² + b x 1
⇔ log 2 = b x log 3 + 2b x log 2 + b
⇔ ⁵log 2 = b x ⁵log 3 + 2b x ⁵log 2 + b

³log 25 + ⁵log 4 
= ³log 5² + ⁵log 2²
= 2 x ³log 5 + 2 x ⁵log 2
= 2 x (³log 5 + ⁵log 2)
= 2 x [1/(a x ⁵log 3 + 2a x ⁵log 2 + a) + b x ⁵log 3 + 2b x ⁵log 2 + b]
= 2/(a x ⁵log 3 + 2a x ⁵log 2 + a) + 2(b x ⁵log 3 + 2b x ⁵log 2 + b)

Coba soal dicek lagi ya.

Semangat!