jika 5 log3 = a dan 2 log5 = b . Tentukan nilai dari 15 log20 ?

[tex] ^{5} \: log3 = a \\ ^{2} \: log5 = b \\ \\ ^{15} \: log20 \\ = \frac{ ^{5} \: log20 }{^{5} \: log15} \\ = \frac{ ^{5} \: log(5.4)}{ ^{5} \: log(5.3)} \\ = \frac{ ^{5} \: log 5 + ^{5} log {2}^{2}}{ ^{5} \: log5 + ^{5} log3} \\ = \frac{1 + 2 .\: ^{5} \: log2 }{1 + a } \\ = \frac{1 + 2 \frac{1}{ ^{2} log5} }{1 + a} \\ = \frac{1 + 2 \frac{1}{b} }{1 + a} \\ = \frac{1 + \frac{2}{b} }{1 + a} \\ = \frac{ \frac{b \: + \: 2}{b} }{1 + a} \\ = \frac{b + 2}{b} \times \frac{1}{1 + a} \\ = \frac{b + 2}{b + ab} [/tex]

Semoga membantu :)