Sabtu, 07 Agustus 2010

CONTOH SOAL LOGARITMA dalam MATEMATIKA

1. Jika {}^{a}\log x = 3 dan {}^{3a}\log y = 3. Nilai \frac{y}{x} sama dengan ….

Jawab.
{}^{a}\log x = 3, maka x = a^{3} dan
{}^{3a}\log y = 3, maka y = (3a)^{3}, sehingga

\frac{y}{x}=\frac{3a^{3}}{a^{3}} = 3^{3}=27.

2. Diketahui {}^{2}\log 7 = a, dan {}^{2}\log 3 = b, maka nilai dari {}^{6}\log 14 adalah …. (UN 2009)

Jawab

{}^{6}\log 14 = \frac{{}^{2}\log 14}{{}^{2}\log 6}

{}^{6}\log 14 = \frac{{}^{2}\log( 2.7)}{{}^{2}\log (2.3)}

{}^{6}\log 14 = \frac{{}^{2}\log 2+{}^{2}\log 7}{{}^{2}\log 2+{}^{2}\log 3}

{}^{6}\log 14 = \frac{1+a}{1+b}

3. Jika {}^{2}\log 3 = a , maka {}^{3}\log 8 = ..... (UN 2005)

{}^{3}\log 8 =\frac{{}^{2}\log 8}{{}^{2}\log 3}

{}^{3}\log 8 =\frac{{}^{2}\log 2^{3}}{{}^{2}\log 3}

{}^{3}\log 8 =\frac{3.{}^{2}\log 2}{a}

{}^{3}\log 8 =\frac{3}{a}

Tidak ada komentar:

Poskan Komentar