D. Evaluating Functions and Solving Equations (4 pts) Let G(x) = log,(2x+1)-2 and H(x) =-2+2 log, x. Find all real numbers x for which H(x) = G(x) 1. 2. Aarnie tried to solve the equation e** +e** =12 but got the wrong answer. Here is his first step: %3D In(e**)+ In(e²") = In(12) a. (3 pts) Explain why his first step was wrong. b. (4 pts) Help Aarnie get a correct solution. Show all steps and write the solution in the box provided using exact
D. Evaluating Functions and Solving Equations (4 pts) Let G(x) = log,(2x+1)-2 and H(x) =-2+2 log, x. Find all real numbers x for which H(x) = G(x) 1. 2. Aarnie tried to solve the equation e** +e** =12 but got the wrong answer. Here is his first step: %3D In(e**)+ In(e²") = In(12) a. (3 pts) Explain why his first step was wrong. b. (4 pts) Help Aarnie get a correct solution. Show all steps and write the solution in the box provided using exact
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Certainly! Below is a transcription of the image adjusted for an educational website:
---
**D. Evaluating Functions and Solving Equations**
1. **(4 pts)** Let \( G(x) = \log_3(2x+1) - 2 \) and \( H(x) = -2 + 2\log_3 x \). Find all real numbers \( x \) for which \( H(x) = G(x) \).
2. Aarnie tried to solve the equation \( e^{4x} + e^{2x} = 12 \) but got the wrong answer. Here is his first step:
\[
\ln(e^{4x}) + \ln(e^{2x}) = \ln(12)
\]
a. **(3 pts)** Explain why his first step was wrong.
b. **(4 pts)** Help Aarnie get a correct solution. Show all steps and write the solution in the box provided using *exact* form. (*'Exact' means do NOT approximate logarithms, square roots or fractions with a calculator. For example, \(\sqrt{2}\) is exact. 1.14 is a calculator approximation.*)
---
There are no graphs or diagrams in the image to describe.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39f8ba9b-8fe9-4a22-a6b2-c49df8fae2b8%2F63d9e933-77f4-4086-9960-9530b2997902%2F3ao7mao_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Below is a transcription of the image adjusted for an educational website:
---
**D. Evaluating Functions and Solving Equations**
1. **(4 pts)** Let \( G(x) = \log_3(2x+1) - 2 \) and \( H(x) = -2 + 2\log_3 x \). Find all real numbers \( x \) for which \( H(x) = G(x) \).
2. Aarnie tried to solve the equation \( e^{4x} + e^{2x} = 12 \) but got the wrong answer. Here is his first step:
\[
\ln(e^{4x}) + \ln(e^{2x}) = \ln(12)
\]
a. **(3 pts)** Explain why his first step was wrong.
b. **(4 pts)** Help Aarnie get a correct solution. Show all steps and write the solution in the box provided using *exact* form. (*'Exact' means do NOT approximate logarithms, square roots or fractions with a calculator. For example, \(\sqrt{2}\) is exact. 1.14 is a calculator approximation.*)
---
There are no graphs or diagrams in the image to describe.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
