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Chapter 5: Q. 33 (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.

2x-5=8

Short Answer

Expert verified

The solution of the given equation is x=8

Step by step solution

01

Step 1. Given Function

The given equation is 2x-5=8.

We have to express irrational solutions in exact form and as a decimal rounded to three decimal places.

Also, We have to verify the result using a graphing utility.

02

Step 2. Explanation

鈬�2x鈭�5=8鈬�ln2x鈭�5=ln23鈬�x鈭�5ln2=3ln2鈬�x鈭�5=3鈬�x鈭�5+5=3+5Add5boththesides鈬�x=8

03

Step 3. Verifying the result

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

From the graph, we can see the line intersect at the x-axis at x=8

Hence verified

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