Question

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

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 these rules.

`3\ln(x)-5\ln(c)=\ln(x^(3))-\ln(c^(5))=\ln \left( (x^(3))/(c^(5)) \right)`

Your single logarithm is ...

`\ln \left( (x^(3))/(c^(5)) \right)`