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# How can we write logarithm of 18 to the base 3 in terms of logarithm of 12 to the base 3?

May 5, 2018

${\log}_{3} 18 = {\log}_{3} 12 + {\log}_{3} \left(\frac{3}{2}\right)$
Since ${\log}_{b} \left(p \cdot q\right) = {\log}_{b} p + {\log}_{b} q$
${\log}_{3} 18 = {\log}_{3} \left(12 \cdot \frac{3}{2}\right)$
$\textcolor{w h i t e}{\text{XXX}} = {\log}_{3} \left(12\right) + {\log}_{3} \left(\frac{3}{2}\right)$