Answer
$\log_8 x^{16/3}$
Work Step by Step
Using the properties of logarithms, the given expression, $
2\log_8 x-\dfrac{2}{3}\log_8 x+4\log_8 x
,$ simplifies to
\begin{array}{l}\require{cancel}
2\log_8 x+4\log_8 x-\dfrac{2}{3}\log_8 x
\\\\=
\log_8 x^2+\log_8 x^4-\log_8 x^{\frac{2}{3}}
\\\\=
\log_8 \dfrac{x^2\cdot x^4}{x^{\frac{2}{3}}}
\\\\=
\log_8 x^{2+4-\frac{2}{3}}
\\\\=
\log_8 x^{\frac{6}{3}+\frac{12}{3}-\frac{2}{3}}
\\\\=
\log_8 x^{\frac{16}{3}}
\\\\=
\log_8 x^{16/3}
.\end{array}
