5) 5e3x+4 15
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Topic Video
Question
![**Problem 5**
Solve the exponential equation:
\[ 5e^{3x + 4} = 15 \]
Steps to solve:
1. Begin by isolating the exponential term. Divide both sides of the equation by 5:
\[ e^{3x + 4} = 3 \]
2. Apply the natural logarithm (ln) to both sides to eliminate the base \(e\):
\[ \ln(e^{3x + 4}) = \ln(3) \]
3. Use the logarithm property \( \ln(a^b) = b\ln(a) \):
\[ 3x + 4 = \ln(3) \]
4. Isolate the variable \(x\). Subtract 4 from both sides:
\[ 3x = \ln(3) - 4 \]
5. Finally, divide by 3 to solve for \(x\):
\[ x = \frac{\ln(3) - 4}{3} \]
Therefore, the solution to the equation is:
\[ x = \frac{\ln(3) - 4}{3} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbfc9c6a-8538-4a72-a7a3-8a03419f890c%2Fb31290d6-2f03-44d3-8921-6af63d0f782a%2Fb7ynnu5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 5**
Solve the exponential equation:
\[ 5e^{3x + 4} = 15 \]
Steps to solve:
1. Begin by isolating the exponential term. Divide both sides of the equation by 5:
\[ e^{3x + 4} = 3 \]
2. Apply the natural logarithm (ln) to both sides to eliminate the base \(e\):
\[ \ln(e^{3x + 4}) = \ln(3) \]
3. Use the logarithm property \( \ln(a^b) = b\ln(a) \):
\[ 3x + 4 = \ln(3) \]
4. Isolate the variable \(x\). Subtract 4 from both sides:
\[ 3x = \ln(3) - 4 \]
5. Finally, divide by 3 to solve for \(x\):
\[ x = \frac{\ln(3) - 4}{3} \]
Therefore, the solution to the equation is:
\[ x = \frac{\ln(3) - 4}{3} \]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 5 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning