
To solve:
The given equation algebraically. Round final answer to three decimal places. Use a graphing utility to verify your answer.

Answer to Problem 62E
The solution of our given equation is x≈0.648 .
Explanation of Solution
Given:
An exponential equation: 1000e−4x=75 .
Calculation:
We will use logarithmic properties to solve our given equation as shown below:
1000e−4x=75(Given equation)1000e−4x1000=751000(Dividing both sides by 1000)e−4x=0.075ln(e−4x)=ln(0.075)(Taking natural log on both sides)−4x⋅ln(e)=ln(0.075)(Using log property ln(am)=mln(a))−4x⋅1=ln(0.075)(Using property ln(e)=1)−4x=−2.59026716545−4x−4=−2.59026716545−4(Dividing both sides by −4)x=0.647566791362x≈0.648(Rounding to three decimal places)
Upon graphing our given function, we will get our required graph as shown below:
Upon looking at our given graph, we can see that the solution of our given equation is x≈0.648 .
Chapter 3 Solutions
Precalculus with Limits: A Graphing Approach
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