Question

Write the expression as a single natural logarithm.3 ln x – 5 ln c

Answer 1

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

Your expression makes use of both these rules.
$3\ln(x)-5\ln(c)=\ln(x^{3})-\ln(c^{5})=\ln \left( \dfrac{x^{3}}{c^{5}} \right)$

Your single logarithm is ...
  $\ln \left( \dfrac{x^{3}}{c^{5}} \right)$