Question

4a^2+9b^2=37ab then log(2a+3b)=?

Answer 1

$4a^2+9b^2=37ab\\ \Rightarrow 4a^2+9b^2+12ab=37ab+12ab\\\Rightarrow (2a)^2+(3b)^2+2 \times 2a \times 3b=49ab\\ \Rightarrow (2a+3b)^2 = 49ab\\ \Rightarrow 2a+3b= \sqrt{49ab} \\ \Rightarrow 2a+3b=7 \sqrt{ab}$

$log(2a+3b)=log(7 \sqrt{ab}) = log\ 7+0.5\ log\ ab$