given $a^2+b^2=28ab$ what's $\log_{3} \left(\dfrac{(a+b)^2}{ab}\right)$?
$\log_{3} \left(\dfrac{(a+b)^2}{ab}\right)$
$\log_{3} \left(\dfrac{a^2+b^2+2ab}{ab}\right)$
$\log_{3} \left(\dfrac{a^2+b^2}{ab}+\dfrac{2ab}{ab}\right)$
$\log_{3} \left(\dfrac{28ab}{ab}+\dfrac{2ab}{ab}\right)$
$\log_{3} 30$
Here I tried using properties but couldn't manage to get trough.
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$\log_{3} 3 + \log_{3} 10 = 1 + \log_{3} 10$
$\log_{10} 3 = \dfrac{25}{12} = \dfrac{\log_{3} 3}{\log_{3} 10} = \dfrac{1}{\log_{3}10}$
$\dfrac{12}{25} = \dfrac{1}{\log_{3}10} \implies \log_{3}10 = \dfrac{25}{12}$
$\log_{3} 30 = 1 + \log_{3} 10 = 1 + \dfrac{25}{12}=\dfrac{12+25}{12}=\dfrac{37}{12}$