Jika 2log3=a dan 3log5=b , maka 30log90?

[tex]2log3 = a \\ \frac{log3}{log2} = a \\ log2 = \frac{1}{a} log3 \\ \\ 3log5 = b \\ \frac{log5}{log3} = b \\ log5 = blog3 \\ \\ = 30log90 \\ = \frac{log90}{log90} \\ = \frac{log(2 \times 5 \times {3}^{2}) }{log(2 \times 3 \times 5)} \\ = \frac{log2 +log {3}^{2} + log5}{log2 + log3 + log5} \\ = \frac{ \frac{1}{a} log3 + 2log3 + blog3}{ \frac{1}{a} log3 +log3 + b log3} \\ = \frac{ \frac{1}{a} + 2 + b}{ \frac{1}{a} + 1 + b } \\ = \frac{1 + 2a + ab}{1 + a + ab} [/tex]