Answer
$\log_c \dfrac{p^3\sqrt{t}}{7}$
Work Step by Step
Using the properties of logarithms, the given expression, $
3\log_c p+\dfrac{1}{2}\log_c t-\log_c 7
,$ is equivalent to
\begin{array}{l}\require{cancel}
\log_c p^3+\log_c t^{1/2}-\log_c 7
\\\\=
\log_c p^3+\log_c \sqrt{t}-\log_c 7
\\\\=
\log_c \left( p^3\sqrt{t} \right)-\log_c 7
\\\\=
\log_c \dfrac{p^3\sqrt{t}}{7}
.\end{array}
