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Chapter 5: Q. 47 (page 315)

Solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility.

蟺1-x=ex

Short Answer

Expert verified

The exact solution is x=ln(蟺)1+ln(蟺)and the rounded solution is x鈮�0.534.

Step by step solution

01

Step 1. Given information.

The given equation is:

蟺1-x=ex

02

Step 2. Determine the solution.

The given equation can be written as:

ln蟺1-x=lnex(1-x)ln(蟺)=xln(蟺)-xln(蟺)=xln(蟺)=x+xln(蟺)ln(蟺)=x(1+ln(蟺))ln(蟺)1+ln(蟺)=xx鈮�0.534

The exact solution is x=ln(蟺)1+ln(蟺)and the rounded solution is x鈮�0.534.

03

Step 3. Verify the result by the graphing utility.

Plot the graphs of y1=蟺1-x andy2=ex 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鈮�0.534. Hence, the solution is verified.

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