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Chapter 3: Problem 114

Use a graphing utility to graph and solve the equation. Approximate the result to three decimal places. Verify your result algebraically. $$10-4 \ln (x-2)=0$$

Short Answer

Expert verified
The exact solution to the equation depends on how it appears on your graphing utility, and the exact root should be approximated to three decimal places and then verified algebraically by substituting back into the equation.

Step by step solution

01

Solve the equation graphically

Graph the function \(f(x) = 10-4 \ln (x-2)\) using your graphing utility. From the graph, estimate the x-value where the function crosses the x-axis. This x-value is the solution to the equation.
02

Approximate the solution

After graphing the function, identify the root, which is where the function \(f(x)\) crosses the axis. Let's say the root is approximated to be \(x=a\), where \(a\) is accurate up to three decimal places.
03

Verify the solution algebraically

Plug the approximated root back into the original equation and verify it works. Substitute \(x\) with \(a\) in the equation. If \(10-4 \ln (a-2)\) equals zero, then the approximation is correct.

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