Question

Use a graphing utility to solve each equation. Express your answer rounded to two decimal places.

${\log }_2(x-1)-{\log }_6(x+2)=2$

Short answer

The solution of the given equation is 12.15.

Step-by-step solution

Step 1. Given information.

The given equation is:

${\log }_2(x-1)-{\log }_6(x+2)=2$

Step 2. Determine the solution by the graphing utility.

Plot the graphs of $y_1={\log }_2(x-1)-{\log }_6(x+2)$ and$y_2=2$ on a coordinate plane. The x-coordinate of the intersection point is the solution of the given equation.

The graphs intersect each other at $x\approx 12.148$. After rounding the value to two decimal places $x\approx 12.15$.

Step 3. Conclusion.

The solution of the given equation is 12.15.