We appreciate your visit to What is the solution to the equation below Round your answer to two decimal places 3 cdot e x 11 76 A x 40 98. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Certainly! Let's solve the equation step-by-step:
We have the equation:
[tex]\[3 \cdot e^x = 11.76\][/tex]
To isolate [tex]\(e^x\)[/tex], we first divide both sides of the equation by 3:
[tex]\[e^x = \frac{11.76}{3}\][/tex]
Now, calculate the right-hand side:
[tex]\[e^x = 3.92\][/tex]
Next, to solve for [tex]\(x\)[/tex], we need to take the natural logarithm (ln) of both sides:
[tex]\[\ln(e^x) = \ln(3.92)\][/tex]
Using the property of logarithms that [tex]\(\ln(e^x) = x \cdot \ln(e)\)[/tex], and knowing that [tex]\(\ln(e) = 1\)[/tex], we get:
[tex]\[x = \ln(3.92)\][/tex]
Now, let's find the natural logarithm of 3.92:
[tex]\[x = \ln(3.92) \approx 1.37\][/tex]
So, the solution to the equation [tex]\(3 \cdot e^x = 11.76\)[/tex] is:
[tex]\[x \approx 1.37\][/tex]
Therefore, the correct answer is:
D. [tex]\(x = 1.37\)[/tex]
We have the equation:
[tex]\[3 \cdot e^x = 11.76\][/tex]
To isolate [tex]\(e^x\)[/tex], we first divide both sides of the equation by 3:
[tex]\[e^x = \frac{11.76}{3}\][/tex]
Now, calculate the right-hand side:
[tex]\[e^x = 3.92\][/tex]
Next, to solve for [tex]\(x\)[/tex], we need to take the natural logarithm (ln) of both sides:
[tex]\[\ln(e^x) = \ln(3.92)\][/tex]
Using the property of logarithms that [tex]\(\ln(e^x) = x \cdot \ln(e)\)[/tex], and knowing that [tex]\(\ln(e) = 1\)[/tex], we get:
[tex]\[x = \ln(3.92)\][/tex]
Now, let's find the natural logarithm of 3.92:
[tex]\[x = \ln(3.92) \approx 1.37\][/tex]
So, the solution to the equation [tex]\(3 \cdot e^x = 11.76\)[/tex] is:
[tex]\[x \approx 1.37\][/tex]
Therefore, the correct answer is:
D. [tex]\(x = 1.37\)[/tex]
Thanks for taking the time to read What is the solution to the equation below Round your answer to two decimal places 3 cdot e x 11 76 A x 40 98. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
