Question

What is the value of x in the equation ln (x+6) - ln (2x-1) =1

Answer 1

`\begin{gathered} \ln (x+6)-\ln (2x-1)=1 \\ \text{Take the exponent of both sides of the equation, we get} \end{gathered}`
`\begin{gathered} e^(\ln \lbrack(x+6)-(2x-1)\rbrack)=e^1 \\ \\ \lbrack(x+6)-(2x-1)\rbrack^{}=2.718^{} \end{gathered}`
`\begin{gathered} \text{Clearing the brackets, we get} \\ x+6-2x+1=2.718 \\ \text{Collecting like terms, we get} \\ x-2x+7=2.718 \\ -x=2.718-7 \\ -x=-4.282 \\ \text{Multiplying through by -1, we get} \\ x=4.282 \end{gathered}`