Jika ³log4=a dan ³log5 =b maka tentukan 8log20

[tex] {}^{3} log4 = a \\ {}^{3} log5 = b \\ {}^{8} log20 \\ = \frac{ {}^{3} log20 }{ {}^{3} log8 } \\ = \frac{ {}^{3} log(4 \times 5) }{ {}^{3} log(4 \times 2) } \\ = \frac{ {}^{3} log4 + {}^{3} log5 }{ {}^{3} log4 + {}^{3} log2 } \\ = \frac{a + b}{a + {}^{3} log2 } \\ = \frac{a + b}{a + \frac{ {}^{4} log2 }{ {}^{4} log3 } } \\ = \frac{a + b}{a + \frac{ {}^{3} log4 }{ {}^{2} log4 } } \\ = \frac{a + b}{a + \frac{a}{2} } \\ = \frac{a + b}{ \frac{2a + a}{2} } \\ = (a + b) \div \frac{3a}{2} \\ = \frac{2a + 2b}{3a} [/tex]