MathTutor
Kategori Soal : Matematika - Logaritma Kelas : X (1 SMA) Pembahasan : Diketahui rumus-rumus yang penting dalam logaritma adalah 1. ⁿlog b + ⁿlog a = ⁿlog (b x a); 2. ⁿlog b - ⁿlog a = ⁿlog (b/a); 3. ⁿlog bᵃ = a x ⁿlog b; 4. ᵃlog b = log b/log a = ⁿlog b/ⁿlog a.
Jika ³log 6 = p dan ³log 2 = q, maka ²⁴log 288 = log 288/log 24 = log (36 x 8)/log (6 x 4) = log (6² x 2³)/log (6 x 2²) = (log 6² + log 2³)/(log 6 + log 2²) = (2 x log 6 + 3 x log 2)/(log 6 + 2 x log 2) = (2 x ³log 6 + 3 x ³log 2)/(³log 6 + 2 x ³log 2) = (2 x p + 3 x q)/(p + 2 x q) = (2p + 3q)/(p + 2q)
Kelas : X (1 SMA)
Pembahasan :
Diketahui rumus-rumus yang penting dalam logaritma adalah
1. ⁿlog b + ⁿlog a = ⁿlog (b x a);
2. ⁿlog b - ⁿlog a = ⁿlog (b/a);
3. ⁿlog bᵃ = a x ⁿlog b;
4. ᵃlog b = log b/log a = ⁿlog b/ⁿlog a.
Jika ³log 6 = p dan ³log 2 = q, maka
²⁴log 288
= log 288/log 24
= log (36 x 8)/log (6 x 4)
= log (6² x 2³)/log (6 x 2²)
= (log 6² + log 2³)/(log 6 + log 2²)
= (2 x log 6 + 3 x log 2)/(log 6 + 2 x log 2)
= (2 x ³log 6 + 3 x ³log 2)/(³log 6 + 2 x ³log 2)
= (2 x p + 3 x q)/(p + 2 x q)
= (2p + 3q)/(p + 2q)
Semangat!