Contoh Soal Logaritma Beserta Jawabannya

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Sifat Logaritma – Berikut informasi mengenai kumpulan rumus logaritma beserta contoh soal dan jawaban pembahasannya untuk anda yang ingin belajar Logaritma dalam cabang keilmuan Matematika. Pada ulasan kali ini kami akan memberikan ulasan yang sama dengan ulasan artikel sebelumnya. Selanjutnya pelajari contoh-contoh berikut: Soal No. 1 Jika a = 4, b = 3, dan c = 2, tentukan nilai dari: a). Pembahasan a) Masukkan angka yang diminta soal seperti berikut b) Ubah dulu bentuk pangkatnya menjadi pangkat yang positif biar lebih mudah, baru dimasuk angkanya.

Matematikastudycenter.com-Soal logaritma dan contoh pembahasan kelas 10 SMA. 1 Ubah bentuk pangkat pada soal-soal berikut menjadi bentuk logaritma: a) 2 3 = 8 b) 5 4 = 625 c) 7 2 = 49 Pembahasan Transformasi bentuk pangkat ke bentuk logaritma: Jika b a = c, maka blog c = a a) 2 3 = 8 → 2log 8 = 3 b) 5 4 = 625 → 5log 625 = 4 c) 7 2 = 49 → 7log 49 = 2 Soal No. 2 Tentukan nilai dari: a) 2log 8 + 3log 9 + 5log 125 b) 2log 1/8 + 3log 1/9 + 5log 1/125 Pembahasan a) 2log 8 + 3log 9 + 5log 125 = 2log 2 3 + 3log 3 2 + 5log 5 3 = 3 2log 2 + 2 3log 3 + 3 5log 5 = 3 + 2 + 3 = 8 b) 2log 1/ 8 + 3log 1/ 9 + 5log 1/ 125 = 2log 2 −3 + 3log 3 −2 + 5log 5 −3 = − 3 − 2 − 3 = − 8 Soal No.

3 Tentukan nilai dari a) 4log 8 + 27log 9 b) 8log 4 + 27log 1/9 Pembahasan a) 4log 8 + 27log 9 = 2 2log 2 3 + 3 3log 3 2 = 3/2 2log 2 + 2/3 3log 3 = 3/2 + 2/3 = 9/6 + 4/6 = 13/6 b) 8log 4 + 27log 1/9 2 3log 2 2 + 3 3log 3 −2 = 2/3 2log 2 + (−2/3) 3log 3 = 2/3 − 2/3 = 0 Soal No. 4 Tentukan nilai dari: a) √2log 8 b) √3log 27 Pembahasan a) √2log 8 = 2 1/2log 2 3 = 3/0,5 2log 2 = 3/0,5 = 6 b) √3log 9 = 3 1/2log 3 2 = 2/0,5 3log 3 = 2/0,5 = 4 Soal No. 5 Diketahui: log p = A log q = B Tentukan nilai dari log p 3 q 2 Pembahasan log p 3 q 2 = log p 3 + log q 2 = 3 log p + 2 log q = 3A + 2B Soal No. 6 Diketahui log 40 = A dan log 2 = B, tentukan nilai dari log 20 Pembahasan log 20 = log 40/2 = log 40 − log 2 = A − B Soal No. 7 Diketahui 2log 7 = a dan 2log 3 = b. Tentukan nilai dari 6log 14 Pembahasan 2log 7 = a log 7/ log 2 = a log 7 = a log 2 2log 3 = b log 3 / log 2 = b log 3 = b log 2 6log 14 = log 14/ log6 log 2.7 log 2 + log 7 log 2 + a log 2 log 2 (1 + a) (1 + a) = = = = = log 2. 3 log 2 + log 3 log 2 + b log 2 log 2 (1 + b) (1 + b) Soal No.

8 Diketahui 2log √ (12 x + 4) = 3. Tentukan nilai x Pembahasan 2log √ (12 x + 4) = 3 Ruas kiri bentuknya log, ruas kanan belum bentuk log, ubah dulu ruas kanan agar jadi bentuk log. Ingat 3 itu sama juga dengan 2log 2 3.

Ingat rumus alog a b = b jadi 2log √( 12 x + 4) = 2log 2 3 Kiri kanan sudah bentuk log dengan basis yang sama-sama dua, hingga tinggal menyamakan yang di dalam log kiri-kanan atau coret aja lognya: 2log √( 12 x + 4) = 2log 2 3 √( 12 x + 4) = 2 3 √( 12 x + 4) = 8 Agar hilang akarnya, kuadratkan kiri, kuadratkan kanan. Yang kiri jadi hilang akarnya: 12 x + 4 = 8 2 12x + 4 = 64 12 x = 60 x = 60/ 12 = 5 Soal No. 9 Tentukan nilai dari 3log 5log 125 Pembahasan 3log 5log 125 = 3log 5log 5 3 = 3log 3 = 1 Soal No.

10 Diketahui 2log 3 = m dan 2log 5 = n. Tentukan nilai dari 2log 90 Pembahasan log 3 2log 3 = = m Sehingga log 3 = m log 2 log 2 log 5 2log 5 = = n Sehingga log 5 = n log 2 log 2 log 3 2. 2 2 log 3 + log 5 + log 2 2log 90 = = log 2 log 2 2 m log 2 + n log 2 + log 2 2log 90 = = 2 m + n + 1 log 2 Soal No.

11 Nilai dari A. 6 Pembahasan Dari sifat logaritma berikut: Soal disederhanakan menjadi Soal No.

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12 Nilai dari A. 6 Pembahasan Dari sifat yang sama: Diperoleh hasil.