Question

4a square +9b square = 37ab, then find 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  

Answer 2

Answer:

4a²+9b²=37ab

(2a)²+(3b²)=-12ab+49ab

(2a+3b)²=49ab

log....

log(2a+3b)²=log49ab

2log(2a+3b)=log49ab

log(2a+3b)=1/2log49ab

log(2a+3b)=log7ab

this is your answer ❣️❣️✌️✌️

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