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Chapter 3: Problem 113

Use a graphing utility to graph and solve the equation. Approximate the result to three decimal places. Verify your result algebraically. $$3-\ln x=0$$

Short Answer

Expert verified
The solution will vary based on the graphing utility used. The solution should be checked by substituting it back into the original equation to verify its validity.

Step by step solution

01

Plotting the equation

Plot the equation \(3 - \ln x = 0\) using a graphing utility. The x-coordinate of the point where the graph intersects the x-axis is the approximate solution to the equation.
02

Approximating the solution

From the graph obtained in step 1, identify the x-intercept and approximate the solution to three decimal places.
03

Algebraic verification

To verify the result algebraically, plug the approximate solution from step 2 back into the original equation. If the left-hand side equals the right-hand side, then the solution is correct.

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Most popular questions from this chapter

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Complete the table for the time \(t\) (in years) necessary for \(P\) dollars to triple if interest is compounded continuously at rate \(r\). $$ \begin{array}{|l|l|l|l|l|l|l|} \hline r & 2 \% & 4 \% & 6 \% & 8 \% & 10 \% & 12 \% \\ \hline t & & & & & & \\ \hline \end{array} $$

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