+97 Let a,b be positive real numbers that satisfy
2 + log2(a) = 3 + log3(b) + log6(a+b)
Find (a+b)/ab
+118677 Let me assume base 10
\(2+log(2a)=3+log(3b)+log[6(a+b)]\\ log2+log a=1+log3+logb + log6 + log(a+b) \\ log2 - log3 - log6 -1= logb + log(a+b) - log a \\ log2 - log3 - log6 -log10= log(a+b) - log a + logb \\ log\frac{2}{3*6*10} = log\left[\frac{(a+b)}{a} *b\right] \\ \frac{2}{3*6*10} = \frac{(a+b)}{a} *b\\~\\ \frac{(a+b)}{a} *b=\frac{1}{90} \)
