Question

Rewrite the expression ln3x−4x+2 as a sum, difference, or product of logarithms, and simplify if possible.

Answer 1

By logarithm quotient rule, it is define as:

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

Based on the given problem:

`\begin{gathered} \ln \mleft((3x-4)/(x+2)\mright) \\ \text{The numerator is }3x-4 \\ \text{and the denominator is }x+2 \end{gathered}`

Therefore, we could rewrite it as

`\ln \mleft((3x-4)/(x+2)\mright)=\ln (3x-4)-\ln (x+2)`