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zmudz
 one year ago
Find \(a/b\) when \(2\log{(a 2b)} = \log{a} + \log{b}\).
zmudz
 one year ago
Find \(a/b\) when \(2\log{(a 2b)} = \log{a} + \log{b}\).

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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1hint: I apply the properties of logarithm so I can write: \[{\left( {a  2b} \right)^2} = ab\] so, after a simplification, we have: \[{a^2} + 4{b^2}  4ab = ab\] or \[{a^2}  5ab + 4{b^2} = 0\] now I divide both sides by b^2, so I get: \[{\left( {\frac{a}{b}} \right)^2}  5\left( {\frac{a}{b}} \right) + 4 = 0\] then I make this variable change: \[z = \left( {\frac{a}{b}} \right)\] so I can rewrite the last equation as follows: \[{z^2}  5z + 4\] please solve for z

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1oops.. \[{z^2}  5z + 4 = 0\]
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