Answer
$\log_6 x^{29/4}$
Work Step by Step
Using the properties of logarithms, the given expression, $
5\log_6 x-\dfrac{3}{4}\log_6 x+3\log_6 x
,$ simplifies to
\begin{array}{l}\require{cancel}
5\log_6 x+3\log_6 x-\dfrac{3}{4}\log_6 x
\\\\=
\log_6 x^5+\log_6 x^3-\log_6 x^{\frac{3}{4}}
\\\\=
\log_6 \dfrac{x^5\cdot x^3}{x^{\frac{3}{4}}}
\\\\=
\log_6 x^{5+3-\frac{3}{4}}
\\\\=
\log_6 x^{\frac{20}{4}+\frac{12}{4}-\frac{3}{4}}
\\\\=
\log_6 x^{\frac{29}{4}}
\\\\=
\log_6 x^{29/4}
.\end{array}
