sifat-sifat logaritma ~ AISYAHRIZ

Rabu, 14 November 2018

sifat-sifat logaritma

November 14, 2018 Tidak ada komentar:

Sifat-Sifat Logaritma

Misalkan a, b, dan g bilangan real positif, dengan g ≠ 1, maka berlaku sifat :

1. $^g\log(a.b) = ^g\log{a} + ^g\log{b}$

Contoh :
$^2\log(2.4) = ^2\log{2} + ^2\log{4}$
$^2\log(8) = ^2\log{2} + ^2\log{4}$
$3 = 1 + 2$

2. $^g\log(\frac{a}{b}) = ^g\log{a} - ^g\log{b}$

Contoh :
$^2\log(\frac{8}{4}) = ^2\log{8} - ^2\log{4}$
$^2\log(2) = 3 - 2$
$1 = 1$

3. $^g\log a^n = n \bullet ^g\log a$
Contoh :
$^2\log 4^2 = 2 \bullet ^2\log 4$
$^2\log 16 = 2 \bullet 2$
$4 = 4$

4. $^g\log a = \frac{^p\log a}{^p\log g}$

Contoh :
$^2\log 4 = \frac{^p\log 4}{^p\log 2}$
$2 = \frac{^p\log 4}{^p\log 2}$
Misal kita ambil p = 4
$2 = \frac{^4\log 4}{^4\log 2}$
$2 = \frac{1}{\frac{1}{2}}$
$2 = 2$

Misal kita ambil p = 2
$2 = \frac{^2\log 4}{^2\log 2}$
$2 = \frac{2}{1}$
$2 = 2$

5. $^g\log a = \frac{1}{^a\log g}$

Contoh :
$^2\log 4 = \frac{1}{^4\log 2}$
$2 = \frac{1}{\frac{1}{2}}$
$2 = 2$

6. $^g\log a \times ^a\log b = ^g\log b$

Contoh :
$^2\log 4 \times ^4\log 16 = ^2\log 16$
$2 \times 2 = 4$
$4 = 4$

7. $^g^{n}\log a^m = \frac{m}{n} ^g\log a$

Contoh :
$^2^{2}\log 4^4 = \frac{4}{2} ^2\log 4$
$4\log 256 = 2 \times 2$
$4 = 4$

8. $g^{^g\log a} = a$
Contoh :
$2^{^2\log 4} = 4$
$2^2 = 4$
$4 = 4$

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