Question

Rewrite the expression ln5x−3x+3 as a sum, difference, or product of logarithms, and simplify if possible.

Answer 1

By the logarithm quotient rule:

`\ln \mleft((x)/(y)\mright)=\ln (x)-\ln (y)`

The given could then be rewritten as:

`\begin{gathered} \ln \mleft((5x-3)/(x+3)\mright)\text{ Given} \\ \\ \text{the numerator is }5x-3,\text{ and the denominator is }x+3 \\ \text{therefore we could rewrite it as} \\ \ln (5x-3)-\ln (x+3)\text{ (final answer)} \end{gathered}`