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Chapter 5: Q. 38 (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.

2-x=1.5

Short Answer

Expert verified

x=鈭�log21.5=-ln1.5ln2鈮�-0.585

Step by step solution

01

Step 1. Given information

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

2-x=1.5

02

Step 2. Explanation

Wecansolveusingformulalogaax=x鈬�2鈭�x=1.5鈬�log22鈭�x=log21.5鈬�鈭�x=log21.5鈬�x=鈭�log21.5NowusingformulalogaM=logaMlogbaForbwewilltakeb=eSo,x=鈭�log21.5=-ln1.5ln2鈮�-0.585

03

Step 3. Verifying the result.

Plot the graph of the equation using the graphing utility as shown below

Hence,

The solution of the equation isx=-0.585

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