To find the solution of the equation (x), follow the steps below.
Step 01: Add 8 to both sides of the equation.
[tex]\begin{gathered} \ln (4x-14)-8+8=-5+8 \\ \ln (4x-14)=3 \end{gathered}[/tex]Step 02: Use the base for both sides.
[tex]e^{\ln (4x-14)}=e^3[/tex]Step 03: Solve e^ln=1
[tex]\begin{gathered} 1\cdot(4x-14)=e^3 \\ 4x-14=e^3 \end{gathered}[/tex]Step 04: Add 14 to both sides, then divide the sides by 4.
[tex]\begin{gathered} 4x-14+14=e^3+14 \\ \frac{4x}{4}=\frac{e^3+14}{4} \\ x=\frac{e^3+14}{4} \end{gathered}[/tex]Done! You found the exact solution.
Step 05: To find the aproximate solution, use the value of e.
[tex]\begin{gathered} x=\frac{20.09+14}{4} \\ x=8.52 \end{gathered}[/tex]Answer: x = 8.52.
