Question

In (4x - 14) - 8 = -5Give all solutions to the equation,If there is more than one solution, enter the answers as a comma-separated list.

Answer 1

To find the solution of the equation (x), follow the steps below.

Step 01: Add 8 to both sides of the equation.

`\begin{gathered} \ln (4x-14)-8+8=-5+8 \\ \ln (4x-14)=3 \end{gathered}`

Step 02: Use the base for both sides.

`e^(\ln (4x-14))=e^3`

Step 03: Solve e^ln=1

`\begin{gathered} 1\cdot(4x-14)=e^3 \\ 4x-14=e^3 \end{gathered}`

Step 04: Add 14 to both sides, then divide the sides by 4.

`\begin{gathered} 4x-14+14=e^3+14 \\ (4x)/(4)=(e^3+14)/(4) \\ x=(e^3+14)/(4) \end{gathered}`

Done! You found the exact solution.

Step 05: To find the aproximate solution, use the value of e.

`\begin{gathered} x=(20.09+14)/(4) \\ x=8.52 \end{gathered}`

Answer: x = 8.52.