Sabtu, 29 September 2012

Contoh Soal Logaritma dan Pembahasan

Diposting oleh Indah Aditiya Pratiwi di 15.12
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}

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