waecmaths question:
Simplify ${{\log }_{10}}6-3{{\log }_{10}}3+\tfrac{2}{3}{{\log }_{10}}27$
Option A:
$3{{\log }_{10}}2$
Option B:
${{\log }_{10}}2$
Option C:
${{\log }_{10}}3$
Option D:
$2{{\log }_{10}}3$
waecmaths solution:
$\begin{align} & {{\log }_{10}}6-3{{\log }_{10}}3+\tfrac{2}{3}{{\log }_{10}}27 \\ & ={{\log }_{10}}6-{{\log }_{10}}{{3}^{3}}+{{\log }_{10}}{{({{3}^{3}})}^{\tfrac{2}{3}}} \\ & ={{\log }_{10}}6-{{\log }_{10}}27+{{\log }_{10}}9 \\ & ={{\log }_{10}}\left( \frac{6\times 9}{27} \right)={{\log }_{10}}2 \\\end{align}$
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