Logaritma | LBB Mattplus

Soal 3 : Logaritma

June 18, 2013 — by Mattplus Production

Tentukan nilai log dari :
${}^{6}\textrm{log 36}-{}^{5}\textrm{log}\frac{1}{125}+{}^{\frac{1}{2}}\textrm{log 16}$

Jawab
${}^{6}\textrm{log 36}-{}^{5}\textrm{log}\frac{1}{125}+{}^{\frac{1}{2}}\textrm{log 16}$
$\small ={}^{6}\textrm{log 6}^2 - {}^{5}\textrm{log }\frac{1}{5^{3}} +{}^{2^{-1}}\textrm{log 2}^4$
$\small ={}{}^{6}\textrm{log 6}^2 - {}{}^{5}\textrm{log 5}{^\left ( -3 \right )} + {}{}^{2^{-1}}\textrm{log 2}^4$
$\small ={2}.{}^{6}\textrm{log 6} - \left ({-3} \right ).{}^{5}\textrm{log 5} +\left (\frac{4}{-1} \right ).{}^{2}\textrm{log 2}$
$\small = 2 + 3 - 4 = 1$

Posted in Logaritma. Tags: logaritma, matematika sma kelas X, soal logaritma, soal uas. Leave a Comment »

Soal 2 : Logaritma

June 15, 2013 — by Mattplus Production

Hitunglah nilai log dari $\small {}^{3}\textrm{log 2}+{}^{3}\textrm{log 54}-{}^{3}\textrm{log 4}$
Jawab
Pada bentuk penjumlahan gunakan sifat log :
$\small {}^{a}\textrm{log b}+{}^{a}\textrm{log c}={}^{a}\textrm{log (b}\times c)$
Pada bentuk pengurangan gunakan sifat log :
$\small {}^{a}\textrm{log b}-{}^{a}\textrm{log c}={}^{a}\textrm{log }\left (\frac{b}{c} \right )$
Dengan menggunakan kedua sifat diatas, di dapat :
$\small {}^{a}\textrm{log b}+{}^{a}\textrm{log c}-{}^{a}\textrm{log d}={}^{a}\textrm{log}\left (\frac{b\times c}{d} \right )$
Maka :
$\small {}^{3}\textrm{log 6}+{}^{3}\textrm{log 54}-{}^{3}\textrm{log 4}$
$\small {}^{3}\textrm{log}\frac{(2\times 54)}{4}$
$\small {}^{3}\textrm{log 81}$
$\small {}^{3}\textrm{log 3}^4$
$\small 4\times {}^{3}\textrm{log 3}$
$\small 4\times 1=4$

Posted in Logaritma. Tags: kursus, lbbmattplus, logaritma, matematika, matematika 1 sma, matematika sma kelas X, SBMPTN, SNMPTN, soal-soal logaritma, UAS. Leave a Comment »

Soal 1 : Logaritma

June 14, 2013 — by Mattplus Production

Hitunglah nilai logaritma berikut ini :
$\small {}^{6}\textrm{log 4} + {}^{6}\textrm{log 9}$

Jawab
Untuk menyelesaikan soal ini gunakan sifat log berikut :
$\small {}^{a}\textrm{log b}+{}^{a}\textrm{log c}= {}^{a}\textrm{log(b}\times c)$
Maka :
$\small {}^{6}\textrm{log 4} + {}^{6}\textrm{log 9}$
$\small {}^{6}\textrm{log (4}\times 9)$
$\small {}^{6}\textrm{log 36}$
$\small {}^{6}\textrm{log 6}^2$
$\small 2.{}^{6}\textrm{log 6}=2$

Posted in Logaritma. Tags: lbb mattplus, logaritma, matematika, matematika kelas x, soal sbmptn, soal snmptn, soal uas, soal-soal logaritma. Leave a Comment »

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