Question

32. Solve for x: ln() + ln( − 1) = ln(4)a. x=0 or 5b. x=0c. x=5d. x=3e. There is no solution

Answer 1

To solve this question, we will proceed thus:

`\ln (x)+\ln (x-1)=\ln (4x)`

Simplifying further: (Applying log rules)

`x(x-1)=4x_{}`
`x^2-x=4x`
`\begin{gathered} x^2-x-4x=0 \\ x^2-5x=0 \\ x(x-5)=0 \\ \text{This means that:} \\ x=0\text{ or } \\ x=5 \\ \\ To\text{ verify our solutions, we will put baxk the value of x into the initital } \\ expression\colon \\ \text{When x=0} \\ \ln (0)+\ln (0-1)=\ln (0)\text{ will result in math error:} \\ \text{When x=5} \\ \ln (5)+\ln (5-1)=\ln (4*5)\text{ this will result in actual solutions} \\ \\ So\text{ with this above test, we can conclude that the correct solution is} \\ x=5 \\ \text{The correct answer therefore is C.} \end{gathered}`

Answer = Option C.