jika 2 log 3 =m dan 3 log 5=n nyatakan logaritma 50 log 45 berikut dalam m dan n

[tex] \frac{log \: 45}{log \: 50} \\ = \frac{log \: {3}^{2}.5 }{log \: 2. {5}^{2} } \\ = \frac{3log {3}^{2} + 3log5}{3log2 + 3log {5}^{2} } \\ = \frac{3.1 + n}{ \frac{1}{m} + n} \\ = \frac{(3 + n)}{ \frac{1 + mn}{n} } \\ = (3 + n) \times \frac{n}{(1 + mn)} \\ = \frac{ {n}^{2} + 3 }{mn + 1} [/tex]