Question

Ln(2m 8th power) exapnad in logarithmic expression

Answer 1

The rules are ...
$\Longrightarrow \,\, \ln(a\,b)=\ln(a)+\ln(b)$
$\Longrightarrow \,\, \ln(a^{b})=b\ln(a)$

Your expression makes use of both of these rules.
$\ln(2m^{8})=\ln(2)+\ln(m^{8})=\ln(2)+8\ln(m)$

The expanded form is
  $\ln(2)+8\ln(m)$