Question

Find x using the equation below

Answer 1

\[x=4\log_{6}(^{2\sqrt{6^{3}}})-6\log_{3}(^{3}\sqrt{3^{2}})\]

Answer 2

\[x=4\log_{6} \left( 2\sqrt{6^{3}} \right)-6\log_{3} \left( 3\sqrt{3^{2}} \right)\]
\[x=4\log_{6} \left( 2*6^{\frac{ 3 }{2 }} \right)-6\log_{3} \left( 3*3^{\frac{ 2 }{ 2 }} \right)\]
\[x=\log_{6} \left( 2*6^{\frac{ 3 }{ 2 }} \right)^{4}-\log_{3} \left( 3*3 \right)^{6}\]
\[x=\log_{6} \left( 2 \right)^{4}+\log_{6} \left( 6 \right)^{6}-\log_{3} \left( 3 \right)^{12}\]
\[x=4\log_{6} 2+6\log_{6} 6-12\log_{3} 3=4\log_{6} 2+6*1-12*1=4\log_{6} 2-6\]