Jika ²log3=a dan ³log5=b maka, 15log20=...?

[tex] {}^{2} log3 = a \\ {}^{3} log5 = b \\ \\ {}^{15} log20 \\ {}^{15} log(5 \times 2 \times 2) \\ {}^{15} log5 + {}^{15} log2 + {}^{15} log2 \\ \frac{ {}^{3} log5 }{ {}^{3} log15 } + \frac{ {}^{3} log2 }{ {}^{3} log15 } + \frac{ {}^{3} log2 }{ {}^{3} log15 } \\ \frac{ {}^{3} log5 }{ {}^{3} log5 + {}^{3} log3 } + \frac{ \frac{1}{ {}^{2} log3} }{ {}^{3} log5 + {}^{3} log3 } + \frac{ \frac{1}{ {}^{2} log3 } }{ {}^{3} log5 + {}^{3} log3} \\ \frac{b}{b+ 1} + \frac{ \frac{1}{a} }{b + 1} + \frac{ \frac{1}{a} }{b + 1} \\ \frac{b}{b + 1} + ( \frac{1}{a} \times \frac{1}{b + 1} ) + ( \frac{1}{a} \times \frac{1}{b + 1} ) \\ \frac{b}{b + 1} + \frac{1}{ab + a} + \frac{1}{ab + a} \\ \frac{b}{b + 1} + \frac{2}{ab + a} \\ \frac{b(ab + a) + 2(b + 1)}{(b + 1)(ab + a)} \\ \frac{a {b }^{2} + ab + 2b + 2 }{a {b}^{2} + ab + ab + a } \\ \frac{a {b}^{2} + ab + 2b + 2 }{a {b}^{2} + 2ab + a} [/tex]