(See Solution) Find all real numbers k_1,k_2,k_3 so that the function k_1log x+k_2log (x+1)+k_3log (x+2) is constantly zero for all positive x. You may want


Question: Find all real numbers \({{k}_{1}},{{k}_{2}},{{k}_{3}}\) so that the function \({{k}_{1}}\log x+{{k}_{2}}\log \left( x+1 \right)+{{k}_{3}}\log \left( x+2 \right)\) is constantly zero for all positive x. You may want to differentiate first, to avoid carrying a lot of logarithms around in your calculations.

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