<p style='text-align: justify;'><span style='font-family:Arial,Helvetica,sans-serif'><span style='font-size:14px'><span style='color:#000000'>Logaritma merupakan kebalikan (invers) dari pemangkatan atau eksponen. Logaritma digunakan untuk menentukan besar pangkat dari suatu bilangan pokok. Selain matematika, logaritma juga digunakan untuk menentukan orde reaksi dalam pelajaran laju reaksi kimia atau menentukan koefisien serap bunyi dalam pelajaran akustik.</span></span></span></p> <p style='text-align: justify;'><span style='font-family:Arial,Helvetica,sans-serif'><span style='font-size:14px'><span style='color:#000000'>Pada dasarnya, rumus algortima adalah: a<sup>b</sup> = c ≈ <sup>a</sup>log c = b</span></span></span></p> <p style='text-align: justify;'><span style='font-family:Arial,Helvetica,sans-serif'><span style='font-size:14px'><span style='color:#000000'><span class='marker'>Adapun <strong>sifat - sifat dasar logaritma</strong>:</span><br /> <br /> - ª log a = 1<br /> Contoh soal:<br /> <sup>2</sup>log 2 = <sup>2</sup>log 2<sup>1</sup> = 1<br /> <br /> - ª log 1 = 0<br /> Contoh soal:<br /> <sup>2</sup>log 1 = <sup>2</sup>log 2<sup>0</sup> = 0<br /> <br /> - ª log a = n<br /> Contoh soal:<br /> <sup>3</sup>log 3<sup>4</sup> = 4<br /> <br /> - ª log b = n × ª log b<br /> Contoh soal:<br /> <sup>2</sup>log 4 = <sup>2</sup>log 22 = 2 <sup>2</sup>log 2 = 2.1 = 2<br /> <br /> - ª log b × c = ª log b + ª log c<br /> Contoh soal:<br /> <sup>4</sup>log 32 × 2 = <sup>4</sup>log 32 + <sup>4</sup>log 2 = <sup>4</sup>log 16 + <sup>4</sup>log 2 + <sup>4</sup>log 2 = <sup>4</sup>log 16 + <sup>4</sup>log 4 = 2 + 1 = 3<br /> <br /> - ª log <sup>b</sup>/c = ª log b - ª log c<br /> Contoh soal:<br /> <sup>2</sup>log (16/2) = <sup>2</sup>log 16 - <sup>2</sup>log 2 = 4 - 1 = 3<br /> <br /> - <sup>a^n </sup>log b <sup>m</sup> = <sup>m</sup>/n × ª log b<br /> Contoh soal:<br /> <sup>2^2</sup>log 4<sup>3</sup> = 3/2 . <sup>2</sup>log 4 = 3/2 (2) = 3<br /> <br /> - ª log b = 1 ÷ <sup>b</sup> log a<br /> Contoh soal:<br /> <sup>2</sup>log 8 = 1 / (<sup>8</sup>log 2) = 1 / (<sup>8</sup>log 8<sup>1/3</sup>) = 1/ (1/3) = 3<br /> <br /> - ª log b × <sup>b</sup> log c × <sup>c</sup> log d = ª log d<br /> Contoh soal:<br /> <sup>2</sup>log 4 × <sup>4</sup>log 16 × <sup>16</sup>log 4 = <sup>2</sup>log 4 = <sup>2</sup>log 22 = 2<br /> <br /> - ª log b = <sup>c</sup> log b ÷ <sup>c</sup> log a (Syarat n > 0 dan n ≠ 1)<br /> Contoh soal:<br /> <sup>2</sup>log 16 = (<sup>4</sup>log 16) / (<sup>4</sup>log 2) = (<sup>4</sup>log 4<sup>2</sup>) / (<sup>4</sup>log 4<sup>1/2</sup>) = 2/ (1/2) = 4 </span></span></span></p>