Jambmaths question:
If $6{{\log }_{x}}2-3{{\log }_{x}}3=3{{\log }_{5}}0.2$, find x
Option A:
$\frac{8}{3}$
Option B:
$\frac{4}{3}$
Option C:
$\frac{3}{4}$
Option D:
$\frac{3}{8}$
Jamb Maths Solution:
$\begin{align} & 6{{\log }_{x}}2-3{{\log }_{x}}3=3{{\log }_{5}}0.2 \\ & {{\log }_{x}}{{2}^{6}}-{{\log }_{x}}{{3}^{3}}=3{{\log }_{5}}\left( 0.2 \right) \\ & {{\log }_{x}}64-{{\log }_{x}}27=3{{\log }_{5}}\left( \frac{1}{5} \right) \\ & {{\log }_{x}}64-{{\log }_{x}}27=3\log ({{5}^{-1}}) \\ & {{\log }_{x}}\frac{64}{27}=3(-1){{\log }_{5}}5 \\ & {{\log }_{x}}{{\left( \frac{4}{3} \right)}^{3}}=-3 \\ & 3{{\log }_{x}}\left( \frac{4}{3} \right)=-3 \\ & {{\log }_{x}}\frac{4}{3}=-1 \\ & {{x}^{-1}}=\frac{4}{3},\text{ }x=\frac{3}{4} \\\end{align}$
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