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Indeks and Log

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Submitted By thiruselvam7
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Adakah Indeks dan Log mempunyai persamaan? Bukan begitu maksud 'persamaan' pada tajuk kita kali. Tapi, maksud persamaan ialah dua ungkapan dihubungkan dengan tanda sama dengan ( = ). Gitu dongg.
Contoh ungkapan : x + 4, 6, y - 7. Ini dipanggil ungkapan. Jika persamaan pula : x + 4 = 5.
Ini baru dipanggil satu persamaan.

Ok, soalan persamaan Indeks dan Logaritma merupakan soalan yang agak femes dalam kertas 1 Matematik Tambahan SPM. Pernah satu tahun, soalan log muncul dalam Kertas 2 - 2011.

Apa yang diperlukan seorang pelajar semasa mengendalikan masalah penyelesaian persamaan ini ialah :
1. Kemahiran pemfaktoran
2. Mahir dengan hukum indeks/logaritma
3. Mahir menukarkan dari indeks kepada log dan sebaliknya.
4. Penukaran asas bagi logaritma.

Kemahiran pemfaktoran biasanya diperlukan semasa menjawab soalan persamaan indeks. Kita teruskan kepada contoh :

Berikut merupakan langkah-langkah penyelesaian :

Kalau mengikut pengalaman saya, ramai pelajar pening dengan proses pemfaktoran. Pening? Jika pening, gunakan cara penggantian. Biarkan setiap nombor yang ingin difaktorkan menjadi algebra. Saya ambil contoh yang sama.

Biar lambat asal selamat. Tapi, kalau dah biasa, mesti cepat! Lepas selesai proses pemfaktoran, sila gantikan semula algebra-algebra tersebut dengan nombor asal.

Asas mestilah sama, barulah proses penyelesaian boleh dilakukan.

Contoh lagi :

Nota : Apabila dua nombor mempunyai nilai indeks yang sama, dan dihubungkan dengan operasi darab atau bahagi, maka mereka dapat digabungkan. Sebagai contoh 4 dan 9. Indeks mereka ialah x, dan mereka dihubungkan dengan operasi darab.

Apabila sebelah kiri dan sebelah kanan persamaan mempunyai asas yang sama dan kiri ada satu asas, kanan pun ada satu asas, maka buang asas tersebut dan hanya ambil indeks sahaja.

Jika nilai indeks sama, dan kiri ada satu asas dan kanan pun satu asas ... maka buang indeks, ambil asas sahaja.

Contohnya :

Indeks dah sama, buang jeee .. Teknik sama, kita panggil kaedah perbandingan. Kita banding-banding laa sebelah kanan dan sebelah kiri. Kalau sama, betul la tu. Buang yang sama.

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